bài 19:
a: ĐKXĐ: \(x\notin\left\{3;-3\right\}\)
\(P=\dfrac{x^2-6x+9}{9-x^2}+\dfrac{4x+8}{x+3}\)
\(=\dfrac{-\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}+\dfrac{4x+8}{x+3}\)
\(=\dfrac{-\left(x-3\right)}{x+3}+\dfrac{4x+8}{x+3}\)
\(=\dfrac{-x+3+4x+8}{\left(x+3\right)}=\dfrac{3x+11}{x+3}\)
b: Thay x=7 vào P, ta được:
\(P=\dfrac{3\cdot7+11}{7+3}=\dfrac{21+11}{10}=\dfrac{32}{10}=3,2\)
Bài 18:
a:
ĐKXĐ: \(x\notin\left\{0;3\right\}\)
\(\dfrac{x}{2x-6}+\dfrac{9}{2x\left(3-x\right)}\)
\(=\dfrac{x}{2\left(x-3\right)}-\dfrac{9}{2x\left(x-3\right)}\)
\(=\dfrac{x^2-9}{2x\left(x-3\right)}=\dfrac{\left(x-3\right)\left(x+3\right)}{2x\left(x-3\right)}=\dfrac{x+3}{2x}\)
b:
ĐKXĐ: x<>-1
\(\dfrac{3}{x+1}-\dfrac{3x+2}{x^3+1}\)
\(=\dfrac{3}{x+1}-\dfrac{3x+2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{3\left(x^2-x+1\right)-3x-2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{3x^2-6x+1}{\left(x+1\right)\left(x^2+x+1\right)}\)
c: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{x^2+4x+4}{x^2-4}+\dfrac{x}{2-x}+\dfrac{4-x}{5x-10}\)
\(=\dfrac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}-\dfrac{x}{x-2}+\dfrac{4-x}{5\left(x-2\right)}\)
\(=\dfrac{x+2}{x-2}-\dfrac{x}{x-2}+\dfrac{4-x}{5\left(x-2\right)}\)
\(=\dfrac{2}{x-2}+\dfrac{4-x}{5\left(x-2\right)}=\dfrac{10+4-x}{5\left(x-2\right)}=\dfrac{14-x}{5\left(x-2\right)}\)
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