Làm các câu dc khoanh giúp mình ạ

1) \(\frac{15x}{7y^3} \cdot \frac{2y^2}{x^2}\) Ta có: \[ \frac{15x}{7y^3} \cdot \frac{2y^2}{x^2} = \frac{15x \cdot 2y^2}{7y^3 \cdot x^2} = \frac{30xy^2}{7x^2y^3} = \frac{30}{7xy} \] 2) \(\frac{6x^3}{7y^4} \cdot \frac{35y^2}{24x}\) Ta có: \[ \frac{6x^3}{7y^4} \cdot \frac{35y^2}{24x} = \frac{6x^3 \cdot 35y^2}{7y^4 \cdot 24x} = \frac{210x^3y^2}{168xy^4} = \frac{210x^2}{168y^2} = \frac{5x^2}{4y^2} \] 3) \(\frac{4y^2}{x^4} \cdot \frac{-3x^2}{8y}\) Ta có: \[ \frac{4y^2}{x^4} \cdot \frac{-3x^2}{8y} = \frac{4y^2 \cdot (-3x^2)}{x^4 \cdot 8y} = \frac{-12x^2y^2}{8x^4y} = \frac{-12y}{8x^2} = \frac{-3y}{2x^2} \] 4) \(\frac{-18y^3}{25x^4} : \frac{9y^3}{-15x^2}\) Ta có: \[ \frac{-18y^3}{25x^4} : \frac{9y^3}{-15x^2} = \frac{-18y^3}{25x^4} \cdot \frac{-15x^2}{9y^3} = \frac{-18y^3 \cdot (-15x^2)}{25x^4 \cdot 9y^3} = \frac{270x^2y^3}{225x^4y^3} = \frac{270}{225x^2} = \frac{6}{5x^2} \] J) \(\frac{8y^2}{9x^2} : \frac{4y}{3x^2}\) Ta có: \[ \frac{8y^2}{9x^2} : \frac{4y}{3x^2} = \frac{8y^2}{9x^2} \cdot \frac{3x^2}{4y} = \frac{8y^2 \cdot 3x^2}{9x^2 \cdot 4y} = \frac{24y^2x^2}{36yx^2} = \frac{24y}{36x} = \frac{2y}{3x} \] C) \(\frac{-20x}{3y^2} : \frac{-4x^3}{5y}\) Ta có: \[ \frac{-20x}{3y^2} : \frac{-4x^3}{5y} = \frac{-20x}{3y^2} \cdot \frac{5y}{-4x^3} = \frac{-20x \cdot 5y}{3y^2 \cdot -4x^3} = \frac{-100xy}{-12x^3y^2} = \frac{100}{12x^2y} = \frac{25}{3x^2y} \] 7) \(\frac{(x+4)^2}{4x+12} : \frac{x+4}{3x+9}\) Ta có: \[ \frac{(x+4)^2}{4x+12} : \frac{x+4}{3x+9} = \frac{(x+4)^2}{4(x+3)} \cdot \frac{3(x+3)}{x+4} = \frac{(x+4)^2 \cdot 3(x+3)}{4(x+3) \cdot (x+4)} = \frac{3(x+4)}{4} = \frac{3x+12}{4} \] 8) \(\frac{5x+10}{4x-8} \cdot \frac{4-2x}{x+2}\) Ta có: \[ \frac{5x+10}{4x-8} \cdot \frac{4-2x}{x+2} = \frac{5(x+2)}{4(x-2)} \cdot \frac{2(2-x)}{x+2} = \frac{5(x+2) \cdot 2(2-x)}{4(x-2) \cdot (x+2)} = \frac{10(2-x)}{4(x-2)} = \frac{-10(x-2)}{4(x-2)} = \frac{-10}{4} = \frac{-5}{2} \] 9) \(\frac{x^2-36}{2x+10} \cdot \frac{3}{6-x}\) Ta có: \[ \frac{x^2-36}{2x+10} \cdot \frac{3}{6-x} = \frac{(x-6)(x+6)}{2(x+5)} \cdot \frac{3}{-(x-6)} = \frac{(x-6)(x+6) \cdot 3}{2(x+5) \cdot -(x-6)} = \frac{3(x+6)}{-2(x+5)} = \frac{-3(x+6)}{2(x+5)} \] 10) \(\frac{x^2-4}{x^2-x} : \frac{x^2+2x}{x-1}\) Ta có: \[ \frac{x^2-4}{x^2-x} : \frac{x^2+2x}{x-1} = \frac{(x-2)(x+2)}{x(x-1)} \cdot \frac{x-1}{x(x+2)} = \frac{(x-2)(x+2) \cdot (x-1)}{x(x-1) \cdot x(x+2)} = \frac{x-2}{x^2} \] 1) \(\frac{4(x+3)}{3x^2-x} : \frac{x^2+3x}{1-3x}\) Ta có: \[ \frac{4(x+3)}{3x^2-x} : \frac{x^2+3x}{1-3x} = \frac{4(x+3)}{x(3x-1)} \cdot \frac{1-3x}{x(x+3)} = \frac{4(x+3) \cdot (1-3x)}{x(3x-1) \cdot x(x+3)} = \frac{4(1-3x)}{x^2(3x-1)} = \frac{-4(3x-1)}{x^2(3x-1)} = \frac{-4}{x^2} \] 12) \(\frac{4x+12}{(x+4)^2} : \frac{3(x+3)}{x+4}\) Ta có: \[ \frac{4x+12}{(x+4)^2} : \frac{3(x+3)}{x+4} = \frac{4(x+3)}{(x+4)^2} \cdot \frac{x+4}{3(x+3)} = \frac{4(x+3) \cdot (x+4)}{(x+4)^2 \cdot 3(x+3)} = \frac{4}{3(x+4)} \] 13) \((x^2-25) : \frac{2x+10}{3x-7}\) Ta có: \[ (x^2-25) : \frac{2x+10}{3x-7} = (x-5)(x+5) \cdot \frac{3x-7}{2(x+5)} = \frac{(x-5)(x+5) \cdot (3x-7)}{2(x+5)} = \frac{(x-5)(3x-7)}{2} \] 14) \(\frac{5x-10}{x^2+7} : (2x-4)\) Ta có: \[ \frac{5x-10}{x^2+7} : (2x-4) = \frac{5(x-2)}{x^2+7} \cdot \frac{1}{2(x-2)} = \frac{5(x-2)}{2(x-2)(x^2+7)} = \frac{5}{2(x^2+7)} \] 15) \((4x^2-16) : \frac{3x+6}{7x-2}\) Ta có: \[ (4x^2-16) : \frac{3x+6}{7x-2} = 4(x^2-4) \cdot \frac{7x-2}{3(x+2)} = 4(x-2)(x+2) \cdot \frac{7x-2}{3(x+2)} = \frac{4(x-2)(7x-2)}{3} \] 16) \(\frac{x-y}{y-1} : \frac{x-y}{x-1} \cdot \frac{x-1}{y-1}\) Ta có: \[ \frac{x-y}{y-1} : \frac{x-y}{x-1} \cdot \frac{x-1}{y-1} = \frac{x-y}{y-1} \cdot \frac{x-1}{x-y} \cdot \frac{x-1}{y-1} = \frac{(x-y) \cdot (x-1) \cdot (x-1)}{(y-1) \cdot (x-y) \cdot (y-1)} = \frac{(x-1)^2}{(y-1)^2} \] 17) \(\frac{x+1}{x+2} \cdot \frac{x+2}{x+3} : \frac{x+3}{x+1}\) Ta có: \[ \frac{x+1}{x+2} \cdot \frac{x+2}{x+3} : \frac{x+3}{x+1} = \frac{x+1}{x+2} \cdot \frac{x+2}{x+3} \cdot \frac{x+1}{x+3} = \frac{(x+1)^2}{(x+3)^2} \] 18) \(\frac{x+1}{x+2} : \frac{x+2}{x+3} \cdot \frac{x+3}{x+1}\) Ta có: \[ \frac{x+1}{x+2} : \frac{x+2}{x+3} \cdot \frac{x+3}{x+1} = \frac{x+1}{x+2} \cdot \frac{x+3}{x+2} \cdot \frac{x+3}{x+1} = \frac{(x+1) \cdot (x+3) \cdot (x+3)}{(x+2) \cdot (x+2) \cdot (x+1)} = \frac{(x+3)^2}{(x+2)^2} \] 19) \(\frac{x+1}{x+2} : \frac{x+2}{x+3} : \frac{x+3}{x+1}\) Ta có: \[ \frac{x+1}{x+2} : \frac{x+2}{x+3} : \frac{x+3}{x+1} = \frac{x+1}{x+2} \cdot \frac{x+3}{x+2} \cdot \frac{x+1}{x+3} = \frac{(x+1) \cdot (x+3) \cdot (x+1)}{(x+2) \cdot (x+2) \cdot (x+3)} = \frac{(x+1)^2}{(x+2)^2} \] 20) \(\frac{x^2+x}{x+2} : \frac{x+3}{x+2} \cdot \frac{x+3}{x+1}\) Ta có: \[ \frac{x^2+x}{x+2} : \frac{x+3}{x+2} \cdot \frac{x+3}{x+1} = \frac{x(x+1)}{x+2} \cdot \frac{x+2}{x+3} \cdot \frac{x+3}{x+1} = \frac{x(x+1) \cdot (x+2) \cdot (x+3)}{(x+2) \cdot (x+3) \cdot (x+1)} = x \] 21) \(\frac{x+1}{x+2} \cdot \left(\frac{x+2}{x+3} : \frac{x+3}{x+1}\right)\) Ta có: \[ \frac{x+1}{x+2} \cdot \left(\frac{x+2}{x+3} : \frac{x+3}{x+1}\right) = \frac{x+1}{x+2} \cdot \left(\frac{x+2}{x+3} \cdot \frac{x+1}{x+3}\right) = \frac{x+1}{x+2} \cdot \frac{(x+2)(x+1)}{(x+3)^2} = \frac{(x+1)^2}{(x+3)^2} \] 22) \(\frac{x-2}{6x+1} \cdot \frac{x^2-2x-3}{x^2-5x+6}\) Ta có: \[ \frac{x-2}{6x+1} \cdot \frac{x^2-2x-3}{x^2-5x+6} = \frac{x-2}{6x+1} \cdot \frac{(x-3)(x+1)}{(x-2)(x-3)} = \frac{(x-2) \cdot (x-3)(x+1)}{(6x+1) \cdot (x-2)(x-3)} = \frac{x+1}{6x+1} \] 23) \(\frac{x+1}{x^2-2x-8} \cdot \frac{4-x}{x^2+x}\) Ta có: \[ \frac{x+1}{x^2-2x-8} \cdot \frac{4-x}{x^2+x} = \frac{x+1}{(x-4)(x+2)} \cdot \frac{4-x}{x(x+1)} = \frac{(x+1) \cdot (4-x)}{(x-4)(x+2) \cdot x(x+1)} = \frac{4-x}{x(x-4)(x+2)} = \frac{-(x-4)}{x(x-4)(x+2)} = \frac{-1}{x(x+2)} \] 24) \(\frac{x^2+2}{4x+24} \cdot \frac{x^2-36}{x^2+x-2}\) Ta có: \[ \frac{x^2+2}{4x+24} \cdot \frac{x^2-36}{x^2+x-2} = \frac{x^2+2}{4(x+6)} \cdot \frac{(x-6)(x+6)}{(x-1)(x+2)} = \frac{(x^2+2) \cdot (x-6)(x+6)}{4(x+6) \cdot (x-1)(x+2)} = \frac{(x^2+2)(x-6)}{4(x-1)(x+2)} \]