Question

simplify $\frac{5a^3b-3ab^2}{3b^2-5a^2b}$

Answer 1

Answer:

$\dfrac{5a^3b-3ab^2}{3b^2-5a^2b}=-a$

Step-by-step explanation:

$\dfrac{5a^3b-3ab^2}{3b^2-5a^2b}$

$\mathrm{Factor}\:5a^3b-3ab^2$

$5a^3b-3ab^2$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c}$

$\gray{a^3=aa^2,\:b^2=bb}$

$=5aa^2b-3abb$

$\gray{\mathrm{Factor\:out\:common\:term\:}ba}$

$=ba\left(5a^2-3b\right)$

$=\dfrac{ba\left(5a^2-3b\right)}{3b^2-5a^2b}$

$\mathrm{Factor}\:3b^2-5a^2b$

$3b^2-5a^2b$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c}$

$\gray{b^2=bb}$

$=3bb-5a^2b$

$\gray{\mathrm{Factor\:out\:common\:term\:}b}$

$=b\left(3b-5a^2\right)$

$=\dfrac{ba\left(5a^2-3b\right)}{b\left(3b-5a^2\right)}$

$\mathrm{Cancel\:}\dfrac{ba\left(5a^2-3b\right)}{b\left(3b-5a^2\right)}$

$\dfrac{ba\left(5a^2-3b\right)}{b\left(3b-5a^2\right)}$

$\gray{3b-5a^2\:=\:-\left(5a^2-3b\right)}$

$=\dfrac{ab\left(5a^2-3b\right)}{-b\left(5a^2-3b\right)}$

$\gray{\mathrm{Refine}}$

$=-\dfrac{ba\left(5a^2-3b\right)}{b\left(5a^2-3b\right)}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:b}$

$=-\dfrac{a\left(5a^2-3b\right)}{5a^2-3b}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:5a^2-3b}$

$=-a$