Question

Solve the equation. Remember to check for extraneous solutions.
x-5/x+5=6/x+5 +5

Answer 1

⇒The first step is to eliminate the fraction by multiplying all the terms with the lowest common denominator.

⇒In this case the lowest common denominator is (x+5), meaning all the terms will be multiplied by (x+5)

⇒
`(x-5)/(x+5) (x+5)=(6)/(x+5) (x+5)+5(x+5)`

⇒Multiply out the brackets.

`x-5=6+5(x)+5(5)\\x-5=6+5x+25`

⇒Group the like terms together and simplify.

`x-5x=6+25+5\\-4x=36\\(-4x)/(-4) =(36)/(-4) \\x=-9`

⇒∴ x=-9