Question

Rezolvati in IR ecuatia:a)$\frac{3}{x-5}- \frac{x}{x+1}= \frac{10}{(x+1)(x-5)};b) \frac{16}{x-2}- \frac{6}{x}= \frac{21}{x+3};c) \frac{x^{2}+x}{x-1}+2x=\frac{3x-1}{x-1}+2 .$

Answer 1

a)
3/(x-5)-x/(x+1)=10/(x+1)(x-5)
3(x+1)-x(x-5)=10
3x+3-x²+5x-10=0
x²-8x+7=0
Δ=(-8)²-4×7=64-28=36
x₁=(8+√64)/2=(8+6)/2=7
x₂=(8-√64)/2=(8-6)/2=1

b)
16/(x-2)-6/x=21/(x+3)
(16x-6x+12)/x(x-2)=21/(x+3)
(10x+12)/(x²-2x)=21/(x+3)
21x²-42x=10x²+12x+30x+36
11x²-84x-36=0
Δ=(-84)²+4×36×11=7056+1584=8640
x₁=(84+√8640)/22=(42+12√15)/11
x₂=(84-√8640)/22=(42-12√15)/11


c)
(x²+x)/(x-1)+2x=(3x-1)/(x-1)+2
x²+x+2x²-2x=3x-1+2x-2
3x²-6x+3=0
x²-2x+1=0
(x-1)²=0
x-1=0
x=1