giúp e với ạ BTVN B3.,B1. Tính (tính nhanh nếu có ),$a)~\frac{-4}7-\frac5{13}.\frac{-39}{25}+\frac{-1}{42}.(\frac{-5}6)$,$b,~\frac29.[\frac{-4}{25}.(\frac1{\sqrt{25}}-\frac2{15})+1\frac23]-\frac{-5}{27}$,$c)~-\frac59.\frac3{11}+\frac{-13}{18}.\frac3{11}+\frac3{11}.$,Bài 2. Tìm x,$a)~(\frac23x-\frac49)(\frac12+\frac{-3}7:x)=0$,$b,~(\frac12-\frac13x)^2=\frac{25}4.$,$c)~\frac12\sqrt x-\frac13=1;d;2x^2-18=0$,$5=2x$ $e)~\frac{x+1}4=\frac{x+2}3$

Question

Thiên Hạo (天昊) · Accepted Answer

Bài 1

a)

$=-\frac{4}{7} - \frac{5}{13} - \frac{39}{25} + \frac{(-1) \cdot (-5)}{42 \cdot 6}$

$= -\frac{4}{7} - \frac{5}{13} - \frac{39}{25} + \frac{5}{252}$

$= \left(-\frac{4}{7} + \frac{5}{252} ight) - \frac{5}{13} - \frac{39}{25}$

$= \left(-\frac{4 \cdot 36}{252} + \frac{5}{252} ight) - \frac{5}{13} - \frac{39}{25}$

$= \frac{-144 + 5}{252} - \frac{5}{13} - \frac{39}{25}$

$= -\frac{139}{252} - \frac{5}{13} - \frac{39}{25}$

$= \frac{-139 \cdot 325 - 5 \cdot 6300 - 39 \cdot 3276}{81900}$

$= \frac{-45175 - 31500 - 127764}{81900}$

$= \frac{-204439}{81900}$

b)

$= \frac{2}{9} \cdot \left[ \frac{-4}{25} \cdot \left( \frac{1}{\sqrt{25}} - \frac{2}{15} ight) + 1\frac{2}{3} ight] - \frac{-5}{27}$

$= \frac{2}{9} \cdot \left[ \frac{-4}{25} \cdot \left( \frac{1}{5} - \frac{2}{15} ight) + \frac{5}{3} ight] + \frac{5}{27}$

$= \frac{2}{9} \cdot \left[ \frac{-4}{25} \cdot \left( \frac{3}{15} - \frac{2}{15} ight) + \frac{5}{3} ight] + \frac{5}{27}$

$= \frac{2}{9} \cdot \left[ \frac{-4}{25} \cdot \frac{1}{15} + \frac{5}{3} ight] + \frac{5}{27}$

$= \frac{2}{9} \cdot \left( \frac{-4}{375} + \frac{625}{375} ight) + \frac{5}{27}$

$= \frac{2}{9} \cdot \frac{621}{375} + \frac{5}{27}$

$= \frac{2 \cdot (9 \cdot 69)}{9 \cdot 375} + \frac{5}{27}$

$= \frac{138}{375} + \frac{5}{27}$

$= \frac{46}{125} + \frac{5}{27}$

$= \frac{46 \cdot 27 + 5 \cdot 125}{3375}$

$= \frac{1242 + 625}{3375}$

$= \frac{1867}{3375}$

c)

$= -\frac{5}{9} \cdot \frac{3}{11} + \frac{-13}{18} \cdot \frac{3}{11} + \frac{3}{11} \cdot 1$

$= \frac{3}{11} \cdot \left( -\frac{5}{9} - \frac{13}{18} + 1 ight)$

$= \frac{3}{11} \cdot \left( -\frac{10}{18} - \frac{13}{18} + \frac{18}{18} ight)$

$= \frac{3}{11} \cdot \frac{-10 - 13 + 18}{18}$

$= \frac{3}{11} \cdot \frac{-5}{18}$

$= \frac{3 \cdot (-5)}{11 \cdot 3 \cdot 6}$

$= \frac{-5}{66}$

Bài 2

a) $(\frac{2}{3}x - \frac{4}{9}) (\frac{1}{2} + \frac{-3}{7} : x) = 0$

Điều kiện: $x eq 0$

Trường hợp 1:

$\frac{2}{3}x - \frac{4}{9} = 0$

$\frac{2}{3}x = \frac{4}{9}$

$x = \frac{4}{9} : \frac{2}{3}$

$x = \frac{2}{3}$ (thỏa mãn điều kiện)

Trường hợp 2:

$\frac{1}{2} + \frac{-3}{7} : x = 0$

$\frac{-3}{7} : x = -\frac{1}{2}$

$x = \frac{-3}{7} : \left(-\frac{1}{2} ight)$

$x = \frac{6}{7}$ (thỏa mãn điều kiện)

Vậy $x \in \left\{\frac{2}{3}; \frac{6}{7} ight\}$.

b) $(\frac{1}{2} - \frac{1}{3}x)^2 = \frac{25}{4}$

$(\frac{1}{2} - \frac{1}{3}x)^2 = \left(\frac{5}{2} ight)^2$

Trường hợp 1:

$\frac{1}{2} - \frac{1}{3}x = \frac{5}{2}$

$\frac{1}{3}x = \frac{1}{2} - \frac{5}{2}$

$\frac{1}{3}x = -2$

$x = -6$

Trường hợp 2:

$\frac{1}{2} - \frac{1}{3}x = -\frac{5}{2}$

$\frac{1}{3}x = \frac{1}{2} - \left(-\frac{5}{2} ight)$

$\frac{1}{3}x = 3$

$x = 9$

Vậy $x \in \{-6; 9\}$.

c) $\frac{1}{2}\sqrt{x} - \frac{1}{3} = 1$

Điều kiện: $x \ge 0$

$\frac{1}{2}\sqrt{x} = 1 + \frac{1}{3}$

$\frac{1}{2}\sqrt{x} = \frac{4}{3}$

$\sqrt{x} = \frac{4}{3} : \frac{1}{2}$

$\sqrt{x} = \frac{8}{3}$

$x = \left(\frac{8}{3} ight)^2$

$x = \frac{64}{9}$ (thỏa mãn điều kiện)

Vậy $x = \frac{64}{9}$.

d) $2x^2 - 18 = 0$

$2x^2 = 18$

$x^2 = 9$

$x = 3$ hoặc $x = -3$.

Vậy $x \in \{3; -3\}$.

e) $\frac{x+1}{4} = \frac{x+2}{3}$

$3(x+1) = 4(x+2)$

$3x + 3 = 4x + 8$

$4x - 3x = 3 - 8$

$x = -5$

Vậy $x = -5$.

Timi · Answer

a) Ta có:
$$
\frac{-4}{7} - \frac{5}{13} \cdot \frac{-39}{25} + \frac{-1}{42} \cdot \left( \frac{-5}{6} \right)
$$

Tính từng phần:
$$
\frac{5}{13} \cdot \frac{-39}{25} = \frac{5 \cdot (-39)}{13 \cdot 25} = \frac{-195}{325} = \frac{-39}{65} = \frac{-3}{5}
$$

$$
\frac{-1}{42} \cdot \left( \frac{-5}{6} \right) = \frac{-1 \cdot (-5)}{42 \cdot 6} = \frac{5}{252}
$$

Gộp lại:
$$
\frac{-4}{7} - \frac{-3}{5} + \frac{5}{252}
$$

Quy đồng mẫu số:
$$
\frac{-4}{7} = \frac{-4 \cdot 36}{7 \cdot 36} = \frac{-144}{252}
$$
$$
\frac{-3}{5} = \frac{-3 \cdot 50.4}{5 \cdot 50.4} = \frac{-151.2}{252}
$$

Cộng các phân số:
$$
\frac{-144}{252} + \frac{151.2}{252} + \frac{5}{252} = \frac{-144 + 151.2 + 5}{252} = \frac{12.2}{252} = \frac{61}{126}
$$

b) Ta có:
$$
\frac{2}{9} \left[ \frac{-4}{25} \left( \frac{1}{\sqrt{25}} - \frac{2}{15} \right) + 1 \frac{2}{3} \right] - \frac{-5}{27}
$$

Tính từng phần:
$$
\frac{1}{\sqrt{25}} = \frac{1}{5}
$$
$$
\frac{1}{5} - \frac{2}{15} = \frac{3}{15} - \frac{2}{15} = \frac{1}{15}
$$

$$
\frac{-4}{25} \cdot \frac{1}{15} = \frac{-4}{375}
$$

$$
1 \frac{2}{3} = \frac{5}{3}
$$

Gộp lại:
$$
\frac{-4}{375} + \frac{5}{3} = \frac{-4}{375} + \frac{5 \cdot 125}{3 \cdot 125} = \frac{-4}{375} + \frac{625}{375} = \frac{621}{375}
$$

$$
\frac{2}{9} \cdot \frac{621}{375} = \frac{2 \cdot 621}{9 \cdot 375} = \frac{1242}{3375}
$$

$$
\frac{1242}{3375} - \frac{-5}{27} = \frac{1242}{3375} + \frac{5 \cdot 125}{27 \cdot 125} = \frac{1242}{3375} + \frac{625}{3375} = \frac{1867}{3375}
$$

c) Ta có:
$$
-\frac{5}{9} \cdot \frac{3}{11} + \frac{-13}{18} \cdot \frac{3}{11} + \frac{3}{11}
$$

Nhóm các số lại:
$$
\frac{3}{11} \left( -\frac{5}{9} - \frac{13}{18} + 1 \right)
$$

Quy đồng mẫu số:
$$
-\frac{5}{9} = -\frac{10}{18}
$$

$$
-\frac{10}{18} - \frac{13}{18} + 1 = -\frac{23}{18} + 1 = -\frac{23}{18} + \frac{18}{18} = -\frac{5}{18}
$$

Gộp lại:
$$
\frac{3}{11} \cdot -\frac{5}{18} = -\frac{15}{198} = -\frac{5}{66}
$$

Đáp số:
a) $\frac{61}{126}$
b) $\frac{1867}{3375}$
c) $-\frac{5}{66}$

Bài 2.
a) $(\frac{2}{3}x-\frac{4}{9})(\frac{1}{2}+\frac{-3}{7}:x)=0$
Ta có tích của hai thừa số bằng 0 thì ít nhất một thừa số phải bằng 0.
- Nếu $\frac{2}{3}x-\frac{4}{9}=0$ thì $\frac{2}{3}x=\frac{4}{9}$
$x=\frac{4}{9}\times \frac{3}{2}$
$x=\frac{2}{3}$
- Nếu $\frac{1}{2}+\frac{-3}{7}:x=0$ thì $\frac{-3}{7}:x=-\frac{1}{2}$
$x=\frac{-3}{7}:\frac{-1}{2}$
$x=\frac{6}{7}$
Vậy $x=\frac{2}{3}$ hoặc $x=\frac{6}{7}$

b) $(\frac{1}{2}-\frac{1}{3}x)^2=\frac{25}{4}$
$(\frac{1}{2}-\frac{1}{3}x)^2=(\frac{5}{2})^2$
$\frac{1}{2}-\frac{1}{3}x=\frac{5}{2}$ hoặc $\frac{1}{2}-\frac{1}{3}x=\frac{-5}{2}$
- Nếu $\frac{1}{2}-\frac{1}{3}x=\frac{5}{2}$ thì $\frac{1}{3}x=\frac{1}{2}-\frac{5}{2}$
$\frac{1}{3}x=\frac{-4}{2}$
$x=\frac{-4}{2}\times 3$
$x=-6$
- Nếu $\frac{1}{2}-\frac{1}{3}x=\frac{-5}{2}$ thì $\frac{1}{3}x=\frac{1}{2}+\frac{5}{2}$
$\frac{1}{3}x=\frac{6}{2}$
$x=\frac{6}{2}\times 3$
$x=9$
Vậy $x=-6$ hoặc $x=9$

c) $\frac{1}{2}\sqrt{x}-\frac{1}{3}=1$
$\frac{1}{2}\sqrt{x}=1+\frac{1}{3}$
$\frac{1}{2}\sqrt{x}=\frac{4}{3}$
$\sqrt{x}=\frac{4}{3}\times 2$
$\sqrt{x}=\frac{8}{3}$
$x=(\frac{8}{3})^2$
$x=\frac{64}{9}$

d) $2x^2-18=0$
$2x^2=18$
$x^2=18:2$
$x^2=9$
$x=\sqrt{9}$
$x=3$ hoặc $x=-3$

e) $\frac{x+1}{4}=\frac{x+2}{3}$
Ta có $\frac{x+1}{4}=\frac{x+2}{3}$
$\frac{x+1}{4}=\frac{x+1+1}{3}$
$\frac{x+1}{4}=\frac{x+1}{3}+\frac{1}{3}$
$\frac{x+1}{4}-\frac{x+1}{3}=\frac{1}{3}$
$\frac{(x+1)\times 3-(x+1)\times 4}{12}=\frac{1}{3}$
$\frac{(x+1)\times (3-4)}{12}=\frac{1}{3}$
$\frac{(x+1)\times (-1)}{12}=\frac{1}{3}$
$\frac{x+1}{12}=\frac{1}{3}\times (-1)$
$\frac{x+1}{12}=\frac{-1}{3}$
$x+1=\frac{-1}{3}\times 12$
$x+1=-4$
$x=-4-1$
$x=-5$