Question

Simplify the rational expression below. When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between your characters. \frac{\left(x^2-16\right)}{\left(x^2-5x+4\right)} The numerator is AnswerThe denominator is AnswerQuestion 2Not yet answeredPoints out of 2.00 Not flaggedFlag questionQuestion textSimplify the rational expression below. When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between your characters. \frac{\left(6a^2-24a+24\right)}{\left(6a^2-24\right)} The numerator is AnswerThe denominator is AnswerQuestion 3Not yet answeredPoints out of 2.00 Not flaggedFlag questionQuestion textMultiply the rational expressions and express the product in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(x^2-x-6\right)}{\left(2x^2+x-6\right)}\cdot \frac{\left(2x^2+7x-15\right)}{\left(x^2-9\right)}The numerator is AnswerThe denominator is AnswerQuestion 4Not yet answeredPoints out of 2.00 Not flaggedFlag questionQuestion textMultiply the rational expressions and express the product in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(2x^2+9x-35\right)}{\left(x^2+10x+21\right)}\cdot \frac{\left(3x^2+2x-21\right)}{\left(3x^2+14x-49\right)}The numerator is AnswerThe denominator is Answer Not flaggedFlag questionQuestion textDivide 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(q^2-9\right)}{\left(q^2+6q+9\right)}\div \frac{\left(q^2-2q-3\right)}{\left(q^2+2q-3\right)}The numerator is AnswerThe denominator is Answer◀︎ L6_07 Simplify a Complex Fraction (Variables)

Answer 1

Given the expression:

`(\left(x^2-16\right))/(\left(x^2-5x+4\right))`

Factor both the numerator and denominator

so,

`\begin{gathered} (x^2-16)=(x-4)(x+4) \\ (x^2-5x+4)=(x-4)(x-1) \end{gathered}`

So, the expression will be:

`(\left(x^2-16\right))/(\left(x^2-5x+4\right))=((x-4)(x+4))/((x-4)(x-1))=(x+4)/(x-1)`

So, the answer will be:

The numerator is x+4

The denominator is x-1