Question

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

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

c)\(\frac{x +1}{x-2}+\frac{x-1}{x +2}=\frac{2\left(x^{2^{ }}+2\right)}{x^2-4}\)

d)(2x+3)\(\left(\frac{3x+8}{2-7x}+1\right)=\left(x-5\right)\left(\frac{3x+8}{2-7x}+1\right)\)

Answer 1

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

<=> \(\frac{x\left(x+2\right)}{x\left(x-2\right)}-\frac{1\left(x-2\right)}{x\left(x-2\right)}=\frac{2}{x\left(x-2\right)}\)

<=> x²+2x-x+2=2

<=> x²+x=2-2

<=> x²+x=0

<=>x(x+1)=0

<=>x=0 hoặc x+1=0

<=>x=0 hoặc x = -1

Answer 2

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

<=>\(\frac{1.x}{x\left(2x-3\right)}-\frac{3}{x\left(2x-3\right)}=\frac{5\left(2x-3\right)}{x\left(2x-3\right)}\)

<=> x-3 =10x-15

<=> x-10x= -15+3

<=> -9x = -12

<=> x = \(\frac{-12}{-9}\)

<=> x = \(\frac{4}{3}\)