Question

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Answer 1

Answer:

Sum of $\frac{7x}{x^2-4}$ and $\frac{2}{x+2}$ is $\mathbf{\frac{9x-4}{x^2-4}}$

Option B is correct answer.

Step-by-step explanation:

We need to find sum of $\frac{7x}{x^2-4}$ and $\frac{2}{x+2}$

Finding sum of  $\frac{7}{x^2-4}$ and $\frac{2}{x+2}$:

$\frac{7x}{x^2-4}+\frac{2}{x+2}$

We know that $x^2-4 =(x+2)(x-2)$

Replacing x^2-4

$\frac{7x}{(x+2)(x-2)}+\frac{2}{x+2}$

Now, taking LCM of (x+2)(x-2) and (x+2) we get (x+2)(x-2)

$=\frac{7x+2(x-2)}{(x+2)(x-2)}\\=\frac{7x+2x-4}{(x+2)(x-2)}\\=\frac{9x-4}{(x+2)(x-2)}\\=\frac{9x-4}{x^2-4}$

So, Sum of $\frac{7x}{x^2-4}$ and $\frac{2}{x+2}$ is $\mathbf{\frac{9x-4}{x^2-4}}$

Option B is correct answer.