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Solve the equation Solution: Given equation: $\frac{4}{x} -3=\frac{5}{2x+3} ;\ x
eq 0,-3/2,\ for\ x.$
Given: Equation: $\frac{4}{x} -3=\frac{5}{2x+3} ;\ x\
eq 0,\ \frac{-3}{2}$
eq 0,\ \frac{-3}{2}$
To do: To solve the given equation for $x$.
Solution:
Here given equation is : $\frac{4}{x} -3=\frac{5}{2x+3} ;\ x\
eq 0,\ \frac{-3}{2}$
eq 0,\ \frac{-3}{2}$
$\frac{4}{x} -3=\frac{5}{2x+3} ;\ x\
eq 0,\ \frac{-3}{2}$
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 $x=-2,\ 1$
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