2 x 1 3 2x 2 23 5x

Asked by admin @ in Math viewed by 587 People

Solve for x 2/x+1 + 3/2(x-2) =23/5x , x not equal to 0,-1,2

Answered by admin @


The value of x is 4 or -2.09

Solution:

Given that solve for "x"

\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5x}

On cross multiplication we get,

\frac{2 \times 2 \times(x-2)+3 \times(x+1)}{(x+1) \times 2 \times(x-2)}=\frac{23}{5x}

On simplification we get,

\frac{4 \times(x-2)+3 \times(x+1)}{(x+1) \times 2 \times(x-2)}=\frac{23}{5 x}

\begin{array}{c}{\frac{4 x-8+3 x+3}{(x+1) \times 2 \times(x-2)}=\frac{23}{5 x}} \\\\ {\frac{7 x-5}{(x+1) \times 2 \times(x-2)}=\frac{23}{5 x}}\end{array}

Again on cross multiplication we get,

\begin{array}{l}{(7 x-5) \times(5 x)=23 \times 2 \times(x+1) \times(x-2)} \\\\ {35 x^{2}-25 x=46 x\left(x^{2}-1 x-2\right)} \\\\ {35 x^{2}-25 x=46 x^{2}-46 x-92} \\\\ {46 x-25 x=46 x^{2}-35 x^{2}-92} \\\\ {21 x=11 x^{2}-92} \\\\ {11 x^{2}-21 x-92=0}\end{array}

Let us use quadratic formula to solve for "x"

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Here a = 11 and b = -21 and c = -92

x= \frac{21 \pm \sqrt{441+4048}}{2 \times 11} \\\\ x=\frac{21 \pm \sqrt{4489}}{22} \end{aligned}

x=\frac{21 \pm 67}{22}

\begin{array}{l}{\text { Now, } x=\frac{21+67}{22}=4} \\\\ {\text {Or}} \\\\ {x=\frac{21-67}{22}=-2.09}\end{array}

Hence, the value of x is 4 or -2.09

Learn more about solve for "x"

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