How do you solve $\frac{2}{x} + \frac{1}{x + 1} = \frac{5}{x^{2} + x}$ $2/x + 1/(x+1) = 5/(x^2+x)$ ?

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How do you solve $\frac{2}{x} + \frac{1}{x + 1} = \frac{5}{x^{2} + x}$ $2/x + 1/(x+1) = 5/(x^2+x)$ ?

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Answer 1 · 2015-06-04T20:26:28

You may have noticed, that $x^{2} + x = x \cdot (x + 1)$ $x^2+x=x*(x+1)$

So we may multiply every part of the equation by $x \cdot (x + 1)$ $x*(x+1)$ and get rid of all the denominators.
BUT: $x \neq 0 and x \neq - 1$ $x!=0andx!=-1$ or one of the denominators $= 0$ $=0$

The equation goes into:
$\to 2 \cdot (x + 1) + x = 5 \to 3 x = 3 \to$ $->2*(x+1)+x=5->3x=3->$ $x = 1$ $x=1$
And this is allowed.

Always check the answer:

$\frac{2}{1} + \frac{1}{1 + 1} = \frac{5}{1^{2} + 1} = 2 \frac{1}{2}$ $2/1+1/(1+1)=5/(1^2+1)=2 1/2$

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How do you solve $\frac{2}{x} + \frac{1}{x + 1} = \frac{5}{x^{2} + x}$ $2/x + 1/(x+1) = 5/(x^2+x)$ ?

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How do you solve 2/x + 1/(x+1) = 5/(x^2+x)2x+1x+1=5x2+x2/x + 1/(x+1) = 5/(x^2+x)?

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How do you solve $\frac{2}{x} + \frac{1}{x + 1} = \frac{5}{x^{2} + x}$ $2/x + 1/(x+1) = 5/(x^2+x)$ ?