Question

Which of the following is the simplified form of the expression (2/x^2-5x+6)+(x/5x-10)?
a) 1/x-2
b) x+10/5(x-2)
c) x^2+7/5(x-2)(x-3)
d) x^2-3x+10/5(x-2)(x-3)

Answer 1

D

Answer 2

\[x ^{2}-5x+6 = (x-2)(x-3), 5x-10 = 5(x-2)\]
\[1/(x-2)[2/(x-3)+x/2] = 1/(x-2)[2\times5 +x \times(x-3)]\times1/(x-3)\]
\[1/(x-2)(x-3)[x ^{2}-3x+10]\]