How do you add \frac { x } { x + 3} + \frac { 6x - 2} { x - 3}?

1 Answer
Dec 29, 2016

x/(x+3)+(6x-2)/(x-3)=(7x^2+13x-6)/(x^2-9)

Explanation:

Step 1: Find the least common multiple of all denominators

x+3 and x-3 have no shared factors, so their least common multiple is their product: (x+3)(x-3)

Step 2: Multiply each term by an appropriate 1 to give them common denominators

x/(x+3) = x/(x+3) * (x-3)/(x-3)= (x(x-3))/((x+3)(x-3))

(6x-2)/(x-3) = (6x-2)/(x-3) * (x+3)/(x+3) = ((6x-2)(x+3))/((x+3)(x-3))

Step 3: Add the numerators of the new fractions

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

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

Step 4: Simplify

(x(x-3)+(6x-2)(x+3))/((x+3)(x-3)) = ((x^2-3x)+(6x^2+16x-6))/(x^2-9)

=(7x^2+13x-6)/(x^2-9)