Given,
The expression is:
[tex]\frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}[/tex]
Required:
The simplified rational expression.
Simplifying the expression,
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}=\frac{x^2+4x-2x-8}{x^2+6x-2x-12}\times\frac{5x+30}{x+5} \\ =\frac{x(x+4)-2(x+4)}{x(x+6)-2(x+6)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)(x-2)}{(x+6)(x-2)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)}{1}\times\frac{5}{x+5} \\ =\frac{5(x+4)}{x+5} \\ =\frac{5x+20}{x+5} \end{gathered}[/tex]
Hence, the simplified rational expression is (5x+20)/(x+5).
The restriction of the expression is:
[tex]x\ne-5,\text{ 2,-6}[/tex]
