Question

How do you simplify `\frac { x ^ { 2} + 17x } { x ^ { 2} - 5x } + \frac { x ^ { 2} - 6x } { x ^ { 2} - 5x }`?

Answer 1

`(2x+11)/(x-5)`

Explanation:

`x^2-5x!=0=>x (x-5)!=0=>x!=0 and x-5!=0`
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`=>x!=0 and x!=5`
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`(x^2+17x)/(x^2-5x)+(x^2-6x)/(x^2-5x)`
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`=(x^2+17x+x^2-6x)/(x^2-5x)`
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`=(x^2+x^2+17x-6x)/(x^2-5x)`
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`=(2x^2+11x)/(x^2-5x)`
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`=(x (2x+11))/(x (x-5))`
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`=(2x+11)/(x-5)`

Answer 2

`(2x+11)/(x+5)`

Explanation:

First - common factor out x. Then we have:
`[x(x+17)]/[x(x-5)]+[x(x-6)]/[x(x-5)]`

Now you can 'cross out' or 'cancel out' the x variables outside the brackets. Now we have:
`(x+17)/(x-5)+(x-6)/(x-5)`

Now you can collect like terms:
`(2x+11)/(x+5)`