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Perform the following operation and simplify.3x/(4x-1) + 2x/(3x-5)

gudeapp's profile pic

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Perform the following operation and simplify.

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

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giorgiana1976's profile pic

Posted (Answer #2)

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We'll multiply the first fraction by (3x - 5) and the 2nd by (4x-1)
[3x(3x - 5) + 2x(4x-1)]/(4x-1)(3x-5)
We'll remove the brackets:
(9x^2 - 15x + 8x^2 - 2x)/(12x^2 - 20x - 3x + 5)
(17x^2 - 17x)/(12x^2 - 23x + 5)
We'l find the roots of the denominator;
12x^2 - 23x + 5 = 0
x1 = (23+sqrt289)/24
x1 = (23+17)/24
x1 = 5/3
x2 = 1/4
17x(x-1)/(x - 5/3)(x-1/4)

swimma-logan's profile pic

Posted (Answer #3)

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Multiply initial fraction (3x - 5) and the 2nd by (4x-1)
[3x(3x - 5) + 2x(4x-1)]/(4x-1)(3x-5)
Remove brackets:
(9x^2 - 15x + 8x^2 - 2x)/(12x^2 - 20x - 3x + 5)
(17x^2 - 17x)/(12x^2 - 23x + 5)
Square the denomiter;
12x^2 - 23x + 5 = 0
x1 = (23+sqrt289)/24
x1 = (23+17)/24
x1 = 5/3
x2 = 1/4
17x(x-1)/(x - 5/3)(x-1/4)

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