Simplify your answer as much as possible.

Question

(x+6 / 2x-10) - (x+5 / 3x - 5)

I separated them with parenthesis to avoid confusion.

Answer 1

combine the two fractions into one, over a LCD

or think of it as cross multiplying to find the new common numerator

[(x+6)(3x-5) - (2x-10)(x+5)]/(2x-10)(3x-5)

combine like terms

= (3x^2 +13x +20 -2x^2+50)/2(3x^2-20x+25)

factor the denominator

= (x^2 +13x +20)/2(3x-5)(x-5)

UNLESS you really did mean it the way you wrote it with parentheses as written

(x+6/3x -5) - (x+5/3x-5)

combine like terms

= x -x + 6/2x-5/3x -5+5

=3/x -5/3x

which is somewhat simpler

= 9/3x -5/3x

= 4/3x

Answer 2

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