Question

Cho biểu thức P = \(1-\left(\dfrac{16x-x^2}{x^2-4}+\dfrac{3+2x}{x-2}+\dfrac{3x-2}{x+2}\right)\)

a)Rút gọn P

b)Tìm giá trị của P với x = 4

Answer 1

a: \(P=1-\left(\dfrac{16x-x^2+\left(2x+3\right)\left(x+2\right)+\left(3x-2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\right)\)

\(=1-\dfrac{16x-x^2+2x^2+7x+6+3x^2-8x+4}{\left(x+2\right)\left(x-2\right)}\)

\(=1-\dfrac{4x^2+15x+10}{\left(x+2\right)\left(x-2\right)}\)

\(=\dfrac{x^2-4-4x^2-15x-10}{\left(x+2\right)\left(x-2\right)}=\dfrac{-3x^2-15x-14}{x^2-4}\)

b: Khi x=4 thì \(P=\dfrac{-3\cdot4^2-15\cdot4-14}{4^2-4}=\dfrac{-61}{6}\)