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Simplify the complex fraction

Algebra
Tutor: None Selected Time limit: 0 Hours

2014-07-19_9-58-43.png
Jul 19th, 2014

2014-07-19_9-58-43.png

we first consider x-5/x - (-12/x-1), then

x-5/x - (-12/x-1) = x-5/x + 12/x-1

Taking L.C.M x(x-1), we get

[(x-5)(x-1) + x(12)] / x(x-1)

(x^2 - 6x + 5 +12x)/x(x-1)

HENCE   (x^2 + 6x + 5 )/x(x-1)

Now consider x+1/x + x+1/x-1

Taking L.C.M x(x-1), we get

[(x+1)(x-1) + x(x+1)] / x(x-1)

(x^2 -1 + x^2 +x) / x(x-1)

(2x^2 +x -1) / x(x-1)

HENCE    (2x^2 +x -1) / x(x-1)

Now when we put the values x(x-1) will cancel out each other, then we get

(x^2 + 6x + 5 ) / (2x^2 +x -1)

By simplifying above equations, we get

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

Now (x+1) will cancel out each other, then

HENCE (x+5) / (2x-1)

Jul 19th, 2014

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