Question

Divide the rational expression below and record any excluded values

Answer 1

we have the expression

`(3x+6)/(x^2-9x+20)\colon(x^2+7x+10)/(x^2-25)`

Simplify

3x+6=3(x+2)

x^2-25=(x+5)(x-5)

x^2-9x+20=(x-4)(x-5)

x^2+7x+10=(x+5)(x+2)

substitute in the given expression

`(3(x+2))/(\mleft(x-4\mright)\mleft(x-5\mright))\colon(\mleft(x+5\mright)\mleft(x+2\mright))/(\mleft(x+5\mright)\mleft(x-5\mright))`

Multiply in cross

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

Remember that the denominator can not be equal to zero

so

the domain is all real numbers except for the numbers x=4, x=5, x=-5 and x=-2

Simplify

`(3)/((x-4))`