Solve the equation Solution: Given equation: $\frac{4}{x} -3=\frac{5}{2x+3} ;\ x

eq 0,-3/2,\ for\ x.$

Given: Equation: $\frac{4}{x} -3=\frac{5}{2x+3} ;\ x\
eq 0,\ \frac{-3}{2}$

To do: To solve the given equation for $x$.

Solution:

Here given equation is : $\frac{4}{x} -3=\frac{5}{2x+3} ;\ x\
eq 0,\ \frac{-3}{2}$

$\frac{4}{x} -3=\frac{5}{2x+3} ;\ x\
eq 0,\ \frac{-3}{2}$

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

$\Rightarrow ( 4-3x)( 2x+3) =5x$

$\Rightarrow 8x+12-6x^{2} -9x=5x$

$\Rightarrow -6x^{2} -6x+12=0$

$\Rightarrow -6\left( x^{2} +x-2\right) =0$

$\Rightarrow x^{2} +x-2=0$

$\Rightarrow x^{2} +2x-x-2=0$

$x( x+2) -1( x+2) =0$

$( x+2)( x-1) =0$

If $x+2=0$

$\Rightarrow x=-2$

if $x-1=0$

$\Rightarrow x=1$

Therefore $x=-2,\ 1$
 

Updated on: 10-Oct-2022

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