Question

Cho biểu thức P= \(\frac{x+2}{x+3}-\frac{5}{x^{2}+x-6}+\frac{1}{2-x}\)

1.Rút gọn biểu thức P

2.Tìm x để P=\(\frac{-3}{4}\)

3. Tính giá trị biểu thức khi x²-9=0

Answer 1

1. P = \(\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}\)                       ĐKXĐ: \(x\ne-3\),  \(x\ne2\)

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

       = \(\frac{x^2-4}{\left(x+3\right)\left(x-2\right)}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{x+3}{x-2}\)

       = \(\frac{x^2-4-5-x-3}{\left(x+3\right)\left(x-2\right)}\)

       = \(\frac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}\)

       = \(\frac{\left(x-4\right)\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\)

       = \(\frac{x-4}{x-2}\)

2. P=\(\frac{-3}{4}\)

<=> \(\frac{x-4}{x-2}=\frac{-3}{4}\)

<=> 4 ( x - 4 ) = -3  ( x - 2 )

<=> 4x - 16 = -3x + 6

<=> 7x = 2 

<=> x = \(\frac{22}{7}\)

3. \(x^2-9=0\)

<=> ( x -3 ) ( x + 3 ) = 0

<=> \(\orbr{\begin{cases}x=3\left(tm\right)\\x=-3\left(ktm\right)\end{cases}}\)

-> P = \(\frac{3-4}{3-2}\) = -1