Question

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Answer 1

Sum of
`(7x)/(x^2-4)` and
`(2)/(x+2)` is
`\mathbf{(9x-4)/(x^2-4)}`

Option B is correct answer.

Explanation:

We need to find sum of
`(7x)/(x^2-4)` and
`(2)/(x+2)`

Finding sum of
`(7)/(x^2-4)` and
`(2)/(x+2)`:

`(7x)/(x^2-4)+(2)/(x+2)`

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

Replacing x^2-4

`(7x)/((x+2)(x-2))+(2)/(x+2)`

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

`=(7x+2(x-2))/((x+2)(x-2))\\=(7x+2x-4)/((x+2)(x-2))\\=(9x-4)/((x+2)(x-2))\\=(9x-4)/(x^2-4)`

So, Sum of
`(7x)/(x^2-4)` and
`(2)/(x+2)` is
`\mathbf{(9x-4)/(x^2-4)}`

Option B is correct answer.