Question

Cho phân thức A=\(\dfrac{1}{x+5}+\dfrac{2}{x-5}-\dfrac{2x+10}{\left(x+5\right)\left(x-5\right)}\)

a) Rút gọn A

b) Cho A =-3. Tính giá trị của biểu thức 9x²-42+49x

Answer 1

\(\dfrac{1}{x+5}+\dfrac{1}{x-5}-\dfrac{2x+10}{\left(x+5\right)\cdot\left(x-5\right)}=\dfrac{x-5+x+5-2\left(x+5\right)}{\left(x+5\right)\left(x-5\right)}\)

=\(\dfrac{2x-2}{x+5}=\dfrac{2\left(x-1\right)}{x+5}\)

b, Khi A=-3

thì ta có

\(\dfrac{2\left(x-1\right)}{x+5}=-3\)

\(\Leftrightarrow\) \(\dfrac{2\left(x-1\right)}{x+5}=\dfrac{-3\left(x+5\right)}{x+5}\Leftrightarrow2x-2=-3x-15\Leftrightarrow2x+3x=-15+2\Leftrightarrow5x=-13\Rightarrow x=-\dfrac{13}{5}\)