Question

bài 1:giải các phg trình sau

a)\(\dfrac{5x-2}{3}=\dfrac{5-3x}{2}\)

b)\(\dfrac{2x-5}{x+5}=3\)

c)\(\dfrac{x^2-6}{x}=x+\dfrac{3}{x}\)

d)\(\dfrac{\left(x^2+2x\right)-\left(3x+6\right)}{x-3}=0\)

e)\(\dfrac{7x-3}{x-1}=\dfrac{2}{3}\)

các bạn giúp mink nha

Answer 1

\(\dfrac{2x-5}{x+5}=3\)

\(\Leftrightarrow2x-5=3\left(x+5\right)\)

\(\Leftrightarrow2x-5=3x+15\)

\(\Leftrightarrow2x-3x=15+5\)

\(\Leftrightarrow-x=20\)

\(\Leftrightarrow x=-20\)

Answer 2

\(\dfrac{x^2-6}{x}=x+\dfrac{3}{x}\)

\(\Leftrightarrow\dfrac{x^2-6}{x}=\dfrac{x^2+3}{x}\)

\(\Rightarrow x^2-6=x^2+3\)

\(\Leftrightarrow x^2-x^2=3+6\)

\(0=9\)(vô lí )

Vậy phương trình vô nghiệm

Answer 3

\(\dfrac{\left(x^2+2x\right)-\left(3x+6\right)}{x-3}=0\)

\(\Leftrightarrow\dfrac{x\left(x+2\right)-3\left(x+2\right)}{x-3}=0\)

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+2\right)}{x-3}=0\)

\(\Leftrightarrow x+2=0\)

\(\Leftrightarrow x=-2\)

Vậy phương trình có tập nghiệm S =\(\left\{-2\right\}\)

Answer 4

\(\dfrac{5x-2}{3}=\dfrac{5-3x}{2}\)

\(\Leftrightarrow\dfrac{2\left(5x-2\right)}{6}=\dfrac{3\left(5-3x\right)}{6}\)

\(\Leftrightarrow10x-4=15-9x\)

\(\Leftrightarrow10x+9x=15+4\)

\(\Leftrightarrow19x=19\)

\(\Leftrightarrow x=1\)