Perform the indicated operation and simplify your answer 10x

Perform the indicated operation and simplify your answer: 10x^2 - 5x - 30/12x^2 + 9x 6x^2 - x - 15/12x^2 + 11x - 15 Perform the indicated operation and simplify your answer: 8/x - 2 - 5/x + 3 Perform the indicated operation and simplify your answer: 4/x - 6 + 3x - 1/6 - x Solve the equation and show the check of your solution(s). Use the method discussed in Section 6.5 of our text, clearing fractions from the equation first. 5/x - 6 = x/x - 2

Solution

( 10x^2 - 5x -30)/( 12x^2 + 9x) / (6x^2 - x -5)/(12x^2 - 11x - 15)

factorise the num. and den. 5(2x^2 - x -6)/3x(4x +3)   / (6x^2 - 6x -x -5)/( 4x +3)(3x-5)

5(x-2)(2x +3)/3x( 4x +3) /    ( x- 1)(6x+5)/(4x+3)(3x-5)

5(x-2)(2x+3)(3x-5)/(3x(x-1)(6x+5)

cannot be further simplified

8/(x -2) - 5/(x+3)

[ 8(x+3) - 5(x-2)]/(x-2)(x+3)

[3x +24 +10]/(x-2)(x+3)

( 3x +34)/(x-2)(x+3)