Question

How do you solve `6/ (x + 3) = 4/(x - 3)`?

Answer 1

`x=15`

Explanation:

Given
[1]`color(white)("XXX")6/(x+3)=4/(x-3)`

Multiplying both sides by `(x+3)(x-3)`
[2]`color(white)("XXX")(6cancel(x+3)(x-3))/(cancel(x+3))=(4(x+3)(cancel(x-3)))/cancel(x-3)`

[3]`color(white)("XXX")6(x-3) = 4(x+3)`

Simplifying by distribution
[4]`color(white)("XXX")6x-18 = 4x+12`

Add `(18-4x)` to both sides
[5]`color(white)("XXX")2x = 30`

Divide both sides by `2`
[6]#color(white)("XXX")x=15