Question

Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .

Answer 1

Given equation: `4/x-3=5/(2x+3); xne0,-3/2`

`4/x-3=5/(2x+3)`

`=>(4-3x)/x=5/(2x+3)`

⇒(4−3x)(2x+3)=5x

⇒−6x²+8x−9x+12=5x

⇒6x²+6x−12=0

⇒x²+x−2=0

⇒x²+2x−x−2=0

⇒(x+2)(x−1)=0

⇒x+2=0 or x−1=0

⇒x=−2 or x=1

Thus, the solutions of the given equation is − 2 or 1