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Question
`x/(x^2 - 25) - 8/(x^2 + 6x + 5)` gives
Options
`(x^2 - 7x + 40)/((x - 5)(x + 5))`
`(x^2 + 7x + 40)/((x - 5)(x + 5)(x + 1))`
`(x^2 - 7x + 40)/((x^2 - 25)(x + 1))`
`(x^2 + 10)/((x^2 - 25)(x + 1))`
Solution
`(x^2 - 7x + 40)/((x^2 - 25)(x + 1))`
Explanation;
Hint:
`x/(x^2 - 25) - 8/(x^2 + 6x + 5) = x/((x + 5)(x - 5)) - 8/((x + 5)(x+ 1))`
= `(x(x + 1) - 8(x - 5))/((x + 5)(x - 5)(x + 1))`
= `(x^2 + x - 8x + 40)/((x^2 - 25)(x + 1))`
= `(x^2 - 7x + 40)/((x^2 - 25)(x + 1))`
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