Question

Solve for $x:\frac{4}{x}-3=\frac{5}{2x+3}x\ne 0,-\frac{3}{2}$

• A. $-2,1$
• B. $-\frac{1}{2},-2$
• C. $-3,-\frac{2}{3}$
• D. None of these

Answer 1

The correct option is A $-2,1$

Given Equation is

$\frac{4}{x}-3=\frac{5}{2x+3}$ with $x$ not equal to $0$ and $\frac{-3}{2}$

Let us multiply LHS and RHS with $x$ then we get

$4-3x=\frac{5x}{2x+3}$

$⟹4(2x+3)-3x(2x+3)=5x$

$⟹8x+12-6x^2-9x=5x$

$⟹-6x^2-6x+12=0$

Dividing with$-6$

$⟹x^2+x-2=0$

Using Middle Term Splitting, we get

$⟹x^2+2x-x-2=0$

$⟹x(x+2)-1(x+2)=0$

$⟹(x+2)(x-1)=0$

$⟹x=-2$ or $x=1$