Question

How do you solve `-\frac{9}{x - 3} = - \frac{3}{x - 5}`?

Answer 1

Distribute the negative and cross multiply

Explanation:

Distribute the negative to the numerator and cross multiply
`-9(x-5) = -9 x +45`

`-3(x-3)= -3x+9`

Combine like terms by subtracting 45 on both sides of the equation
`-9x +45 = -3x +9`

`-9x=-3x -36`

Combine like terms by adding 3x on both sides of the equations
`-6x=-36`

Isolate x by dividing by -6
`x=6`

Answer 2

`x = 6`

Explanation:

Decide what to do with the negative at the front of each fraction.
It may only be used with the numerator OR the denominator - not both.

`9/(color(red)(-)(x-3)) = (color(red)(-3))/(x-5)" "larr` now cross multiply

`9(x-5) = color(red)(+3)(x-3) " "larr` remove the brackets

`9x-45 = 3x-9 " "larr` re-arrange the terms

`9x-3x = 45-9" "larr` simplify each side

`6x = 36" "larrdiv 6`

`x = 6`

Of course, the simplest solution with the negative signs, is to multiply each fraction by `-1`, or move each to the other side to make each term positive.

`3/(x-5) = 9/(x-3)" "larr` cross multiply and proceed as above.