Question

Solve
X/x+1+x+1/x=34/15, x not=0or-1

Answer 1

Answer:

Required value of x is either - 5 / 2 or 3 / 2.

Step-by-step explanation:

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

From the properties of expansion :

• ( a + b )^2 = a^2 + b^2 + 2ab

$\implies \dfrac{x^2 + x^2 + 1 + 2x }{x^2 + x }=\dfrac{34}{15}\\\\\\\implies \dfrac{2x^2 + 2x + 1 }{x^2 + x } = \dfrac{34}{15}\\\\\\\implies 15(2x^2 + 2x + 1 )=34(x^2 + x )\\\\\\\implies 30x^2 + 30x + 15 = 34x^2 + 34x \\\\\implies 0 = 34x^2 - 30x^2 + 34x - 30x - 15 = 0 \\\\\implies 4x^2 + 4x - 15 = 0\\\\\implies 4x^2 + (10-6)x-15=0\\\\\implies 4x^2+10x-6x-15=0\\\\\implies 2x(2x+5)-3(2x+5)=0\\\\\(2x+5)(2x-3)$

By Using Zero Product Rule :

2x + 5 = 0    Or  2x - 3 = 0

x = - 5 / 2   Or x = 3 / 2

Hence the required value of x is either - 5 / 2 or 3 / 2.