Question

Simplify


`\sf{ \frac{x - 1}{ {x}^(2) - 3x + 2 } + \frac{x - 2}{ {x}^(2) - 5x + 6} + \frac{x - 5}{ {x}^(2) - 8x + 15}}`
Show your work!
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Answer 1

See the answers in pic .............

Answer 2

see below

Explanation:

`(x-1)/(x^2-3x+2)+ (x-2)/(x^2-5x+6) +(x-5)/(x^2-8x+15)`

we need to simplify that

`x^2-3x+2=(x-1)(x-2)\\\\x^2-5x+6=(x-2)(x-3)\\\\x^2-8x+15=(x-3)(x-5)`

so we can continue

`(x-1)/((x-1)(x-2))=(1)/(x-2)\\\\(x-2)/((x-2)(x-3)) =(1)/(x-3)\\\\(x-5)/((x-3)(x-5)) =(1)/(x-3)`

and we can put all together

`(1)/(x-2)+ (1)/(x-3)+ (1)/(x-3)\\\\(1)/(x-2) +(2)/(x-3)\\\\(x-3)/((x-3)(x-2))+ (2(x-2))/((x-2)(x-3)) \\\\(x-3+2x-4)/((x-3)(x-2))\\\\(3x-7)/(x^2-5x+6)`