Question

How do you solve `x- \frac { x } { x + 7} = \frac { 7} { x + 7}`?

Answer 1

You may multiply everthing by `x+7`
(under condition that `x+7!=0`)

Explanation:

`x(x+7)-(x(cancel(x+7)))/(cancel(x+7))=(7(cancel(x+7)))/(cancel(x+7)`

`x(x+7)-x=7->x^2+7x-x=7`

Turn this into a proper quadratic equation:
`x^2+6x-7=0`

Factorize: `(x+7)(x-1)=0`

The solution `x+7=0` is not allowed - it would make the fractions in the original equation undefined.

So the soltion `x-1=0->x=1` is left.

Check:
`1-1/(1+7)=7/(1+7)->1-1/8=7/8`