How do I solve this equation quick with an easy method? (2x-16)/(3x^2-21x+30)+(2)/(3x-15) Thanks! I hope I get an answer ASAP!

Question

How do I solve this equation quick with an easy method?


`(2x-16)/(3x^2-21x+30)+(2)/(3x-15)`

Thanks! I hope I get an answer ASAP!

Answer 1

4/(3(x-2))

Explanation:

3x^2-21x+30=3(x^2-7x+10)=3(x-5)(x-2)

3x-15=3(x-5)

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So the common denominator must be 3(x-5)(x-2)

2(x-2)=2x-4

Add the numerators,

(2x-16)+(2x-4)=4x-16-4=4x-20

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(4x-20)/[3(x-5)(x-2)]

simplify 4x-20 into 4(x-5)

cancel out the (x-5)'s for both the denominator and the numerator

4/[3(x-2)]