Simplify x-x2-3 x-4-4 x-x2-7 x-12

The correct option is A x(5x 1)/(x 1)(x+3)(x+4)x/x^2+3x 4 + 4x/x^2+7x+12 =x/(x 1)(x+4) + nbsp;4x/(x+3)(x+4) L.C.D =(x 1)(x+3)(x+4) = x(x+3)+4x(x 1)/(x 1)(x ...

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Byju's Answer

Standard X

Mathematics

Subtraction of Rational Expressions

Simplify x/x2...

Question

Simplify $\frac{x}{x^{2} + 3 x - 4} + \frac{4 x}{x^{2} + 7 x + 12} .$

\frac{x (5 x - 1)}{(x - 1) (x + 3) (x + 4)}

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\frac{x (5 x + 1)}{(x - 1) (x + 3) (x + 4)}

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\frac{x (5 x - 1)}{(x + 1) (x + 3) (x + 4)}

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\frac{x (5 x + 1)}{(x + 1) (x + 3) (x + 4)}

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Solution

The correct option is A $\frac{x (5 x - 1)}{(x - 1) (x + 3) (x + 4)}$
$\frac{x}{x^{2} + 3 x - 4} + \frac{4 x}{x^{2} + 7 x + 12} = \frac{x}{(x - 1) (x + 4)} + \frac{4 x}{(x + 3) (x + 4)}$

$L . C . D = (x - 1) (x + 3) (x + 4)$

$= \frac{x (x + 3) + 4 x (x - 1)}{(x - 1) (x + 3) (x + 4)}$

$= \frac{5 x^{2} - x}{(x - 1) (x + 3) (x + 4)}$

$= \frac{x (5 x - 1)}{(x - 1) (x + 3) (x + 4)}$

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Simplify xx2+3x−4+4xx2+7x+12.

The correct option is A x(5x−1)(x−1)(x+3)(x+4)xx2+3x−4+4xx2+7x+12=x(x−1)(x+4)+4x(x+3)(x+4) L.C.D=(x−1)(x+3)(x+4) =x(x+3)+4x(x−1)(x−1)(x+3)(x+4) =5x2−x(x−1)(x+3)(x+4) =x(5x−1)(x−1)(x+3)(x+4)

Simplify $\frac{x}{x^{2} + 3 x - 4} + \frac{4 x}{x^{2} + 7 x + 12} .$