How to solve and show as fraction in lowest terms: a) `3/(u+3) + u - 2` b)  `5/(x+3) + 1/( x^2 - 9)` c) ` 2 /(sqrt(x^2+2)) - 5/(x^2+2)`  

Expert Answers

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The expressions have to be solved and expressed in the lowest terms.

`3/(u+3) + u - 2`

=> `(3 + (u - 2)(u + 3))/(u + 3)`

=> `(3 + u^2 - 2u + 3u - 6)/(u + 3)`

=> `(u^2 + u - 3)/(u + 3)`

`5/(x + 3) + 1/(x^2 - 9)`

=> `(5(x - 3) + 1)/(x^2 - 9)`

=> `(5x - 15 + 1)/(x^2 - 9)`

=> `(5x - 14)/(x^2 - 9)`

`2/(sqrt(x^2 + 2)) - 5/(x^2+2)`

=> `(2*sqrt(x^2 + 2) - 5)/(sqrt(x^2 + 2))`

=> `(2*sqrt(x^2 + 2) - 5)/(sqrt(x^2 + 2))`

=> `(2*(x^2 + 2) - 5*sqrt(x^2 + 2))/(x^2 + 2)^(3/2)`

=> `(4x^2 + 4 - 5*sqrt(x^2 + 2))/(x^2 + 2)^(3/2)`

The expressions in the lowest terms are: `3/(u+3) + u - 2 = (u^2 + u - 3)/(u + 3)` , `5/(x + 3) + 1/(x^2 - 9) = (5x - 14)/(x^2 - 9)` and `2/(sqrt(x^2 + 2)) - 5/(x^2+2) = (4x^2 + 4 - 5*sqrt(x^2 + 2))/(x^2 + 2)^(3/2)`

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