Bài 45:
a: ĐKXĐ: x∉{1;-1}
b: \(P=\frac{x}{2x-2}+\frac{x^2+1}{2-2x^2}\)
\(=\frac{x}{2\left(x-1\right)}-\frac{x^2+1}{2\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x\left(x+1\right)-x^2-1}{2\left(x-1\right)\left(x+1\right)}=\frac{x-1}{2\left(x-1\right)\left(x+1\right)}=\frac{1}{2\left(x+1\right)}\)
c: \(P=-\frac12\)
=>\(\frac{1}{2\left(x+1\right)}=-\frac12\)
=>2(x+1)=-2
=>x+1=-1
=>x=-2(nhận)
Bài 46:
a: ĐKXĐ: x∉{0;-5}
b: \(P=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)
\(=\frac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\frac{2\cdot\left(x+5\right)\left(x-5\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)
\(=\frac{x^3+2x^2+2\left(x^2-25\right)+50-5x}{2x\left(x+5\right)}=\frac{x^3+2x^2-5x+50+2x^2-50}{2x\left(x+5\right)}\)
\(=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}=\frac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}\)
\(=\frac{\left(x+5\right)\left(x-1\right)}{2\left(x+5\right)}=\frac{x-1}{2}\)
P=1
=>x-1=2
=>x=3(nhận)
P=-3
=>x-1=-6
=>x=-5(loại)
