Question

Multiply. Stars and restrictions on the variable. Simplify the rational expression.

Answer 1

Given,

The expression is:

`(x^2+2x-8)/(x^2+4x-12)*(5x+30)/(x+5)`

Required:

The simplified rational expression.

Simplifying the expression,

`\begin{gathered} (x^2+2x-8)/(x^2+4x-12)*(5x+30)/(x+5)=(x^2+4x-2x-8)/(x^2+6x-2x-12)*(5x+30)/(x+5) \\ =(x(x+4)-2(x+4))/(x(x+6)-2(x+6))*(5(x+6))/(x+5) \\ =((x+4)(x-2))/((x+6)(x-2))*(5(x+6))/(x+5) \\ =((x+4))/(1)*(5)/(x+5) \\ =(5(x+4))/(x+5) \\ =(5x+20)/(x+5) \end{gathered}`

Hence, the simplified rational expression is (5x+20)/(x+5).

The restriction of the expression is:

`x\\e-5,\text{ 2,-6}`