Question

M=\(\dfrac{x+1}{2x-2}+\dfrac{3}{x^2-1}-\dfrac{x+3}{2x+2}\)

a) Rút gọn M

b) Tính x để M=5

Answer 1

M = \(\dfrac{x+1}{2x-2}+\dfrac{3}{x^2-1}-\dfrac{x+3}{2x+2}\)

= \(\dfrac{x+1}{2\left(x-1\right)}+\dfrac{3}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+3}{2\left(x+1\right)}\)

= \(\dfrac{\left(x+1\right)^2+6-\left(x+3\right)\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}\)

= \(\dfrac{x^2+2x+1+6-x^2-2x+3}{2\left(x-1\right)\left(x+1\right)}\)

= \(\dfrac{10}{2\left(x-1\right)\left(x+1\right)}\)

= \(\dfrac{5}{\left(x-1\right)\left(x+1\right)}\)

b,

Để M = 5

<=> \(\dfrac{5}{\left(x-1\right)\left(x+1\right)}\)= 5

<=> (x - 1)(x + 1) = 1

<=> x² -1 = 1

<=> x² - 2 = 0

<=> (x - \(\sqrt{2}\))(x + \(\sqrt{2}\)) = 0

\(\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\)