Question

How do you solve `\frac { 8} { x - 2} + 3= \frac { x + 6} { x - 2}`?

Answer 1

There is no solution.

Explanation:

Solve:

`8/(x-2)+3=(x+6)/(x-2)`

Multiply both sides by the least common denominator `(x-2)`.

`(x-2)xx(8)/(x-2)+(x-2)xx3=(x+6)/(x-2)xx(x-2)`

Simplify.

`color(red)cancel(color(black)((x-2)))^1xx(8)/color(red)cancel(color(black)((x-2)))^1+(x-2)xx3=(x+6)/color(red)cancel(color(black)((x-2)))^1xxcolor(red)cancel(color(black)((x-2)))^1`

`8+3(x-2)=x+6`

Expand.

`8+3x-6=x+6`

Simplify.

`3x+2=x+6`

Subtract `x` from both sides.

`3x-x+2=6`

Simplify.

`2x+2=6`

Subtract `2` from both sides.

`2x=6-2`

Simplify.

`2x=4`

Divide both sides by `2`.

`x=4/2`

Reduce.

`x=2`

Check

`8/(x-2)+3=(x+6)/(x-2)`

Substitute `2` for `x`.

`8/(2-2)+3=(2+6)/(2-2)`

`8/0+3=8/0`

`n/0` is undefined, and both sides are not equal, so there is no solution.