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:

`(a)/(b)/(c)/(d)=(ad)/(bc)`

Therefore:

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

Using distributive property:

`(9x^4-15x^3-17x^2+43x-20)/(18x^4-30x^3-34x^2+86x-40)`

Factor:

`((3x-4)(3x+5)(x-1)^2)/(2(x-1)^2(3x-4)(3x+5))`

Simplify:

`(1)/(2)`

Answer:

The numerator is 1

The denominator is 2