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

2 Answers
Sep 26, 2016

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

Sep 26, 2016

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.