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Question

Solve the quadratic equation by factorization method.

$$\dfrac { x }{ x+1 } +\dfrac { x+1 }{ x } =\dfrac { 34 }{ 15 } $$


Solution

Given quadratic equation is 
$$\dfrac{x}{x+1}+\dfrac{x+1}{x}=\dfrac{34}{15}$$

$$\implies 15[x^{2}+(x+1)^{2}]=34[x(x+1)]$$

$$\implies 15[2x^{2}+2x+1]=34[x^{2}+x]$$

$$\implies 30x^{2}+30x+15=34x^{2}+34x$$

$$\implies 4x^{2}+4x-15=0$$

$$\implies 4x^{2}+10x-6x-15=0$$

$$\implies 2x(2x+5)-3(2x+5)=0$$

$$\implies (2x+5)(2x-3)=0$$

$$\implies 2x+5=0, 2x-3=0$$

$$\implies x=\dfrac{3}{2}, \dfrac{-5}{2}$$

Mathematics

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