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For x ≠ –2 and x ≠ –4, x/(x + 4) + (-3)/(x + 2) =

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Joined: 02 Sep 2009
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For x ≠ –2 and x ≠ –4, x/(x + 4) + (-3)/(x + 2) =  [#permalink]

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27 Jun 2018, 20:08
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Difficulty:

15% (low)

Question Stats:

93% (01:39) correct 7% (01:58) wrong based on 40 sessions

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For x ≠ –2 and x ≠ –4, $$\frac{x}{x+4}+\frac{-3}{x+2}=$$

A. $$\frac{x^2-x-12}{(x+4)(x+2)}$$

B. $$\frac{-3}{(x+4)(x+2)}$$

C. $$\frac{x-3}{2x+6}$$

D. $$\frac{1}{x+4}$$

E. $$-2$$

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Re: For x ≠ –2 and x ≠ –4, x/(x + 4) + (-3)/(x + 2) =  [#permalink]

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27 Jun 2018, 22:44

Solution

To find:
• The value of the expression $$\frac{x}{x+4} + \frac{-3}{x+2}$$

Approach and Working:
We can simplify the expression in the following manner:
• $$\frac{x}{x+4} + \frac{-3}{x+2}$$
= $$\frac{x(x+2) – 3(x+4)}{(x+2)(x+4)}$$
= $$\frac{x^2 + 2x – 3x -12}{(x+2)(x+4)}$$
= $$\frac{x^2 – x – 12}{(x+2)(x+4)}$$

Hence, the correct answer is option A.

Note: Replacing x = 0, one can easily get the answer without much calculation.
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Re: For x ≠ –2 and x ≠ –4, x/(x + 4) + (-3)/(x + 2) = &nbs [#permalink] 27 Jun 2018, 22:44
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