Question

Divide the rational expressions and express in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(9x^2+3x-20\right)}{\left(3x^2-7x+4\right)}\div \frac{\left(6x^2+4x-10\right)}{\left(x^2-2x+1\right)}The numerator is AnswerThe denominator is Answer

Answer 1

Using the definition of fractions division:

$\frac{a}{b}\div\frac{c}{d}=\frac{ad}{bc}$

Therefore:

$\begin{gathered} \frac{9x^2+3x-20}{3x^2-7x+4}\div\frac{6x^2+4x-20}{x^2-2x+1}=\frac{(9x^2+3x-20)(x^2-2x+1)}{(3x^2-7x+4)(6x^2+4x-10)} \\ \end{gathered}$

Using distributive property:

$\frac{9x^4-15x^3-17x^2+43x-20}{18x^4-30x^3-34x^2+86x-40}$

Factor:

$\frac{(3x-4)(3x+5)(x-1)^2}{2(x-1)^2(3x-4)(3x+5)}$

Simplify:

$\frac{1}{2}$

Answer:

The numerator is 1

The denominator is 2