Question

How do you evaluate `\frac { 5} { x - 3} - \frac { 10} { x + 3} = \frac { 7} { x ^ { 2} - 9}`?

Answer 1

`x=38/5`

Refer to the explanation for the process.

Explanation:

Simplify:

`5/(x-3)-10/(x+3)=7/(x^2-9)`

Simplify `x^2-9^2` using the difference of squares: `a^2-b^2=(a+b)(a-b)`

`x^2-3^2=(x+3)(x-3)`

Rewrite the expression.

`5/(x-3)-10/(x+3)=7/((x+3)(x-3))`

The least common denominator (LCD) for the fractions is `(x+3)(x-3)`. Multiply both sides by the LCD and cancel.

`(x+3)color(red)cancel(color(black)((x-3)))^1xx5/color(red)cancel(color(black)((x-3)))^1-color(red)cancel(color(black)((x+3)))^1(x-3)xx10/color(red)cancel(color(black)((x+3)))^1=color(red)cancel(color(black)((x+3)))^1color(red)cancel(color(black)((x-3)))^1xx7/(color(red)cancel(color(black)((x+3)))^1color(red)cancel(color(black)((x-3)))^1`

Simplify.

`5(x+3)-10(x-3)=7`

Expand.

`5x+15-10x+30=7`

Simplify.

`-5x+45=7`

Subtract `45` from both sides.

`-5x=7-45`

Simplify.

`-5x=-38`

Divide both sides by `-5`.

`x=-(38)/(-5)`

Two negatives make a positive.

#x=38/5