Question

SOLVE BY FACTORIZATION METHOD : x/x+1 + x+1/x=34/15

Answer 1

I hope it can help u.....

Answer 2

$x=-\dfrac{5}{2}$ or $x=\dfrac{3}{2}$

Step-by-step explanation:

We have,

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

To find, the value of x by factorisation method = ?

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

⇒ $\dfrac{x^{2} +x^2+2x+1}{x^2+x}=\dfrac{34}{15}$

⇒ $34(x^2+x)=15(2x^{2}+2x+1)$

⇒ $34x^2+34x=30x^{2}+30x+15$

⇒ $4x^{2} +4x-15=0$

By factorisation method, we get

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

⇒ $2x(2x+5)-3(2x+5)=0$

⇒ $(2x+5)(2x-3)=0$

⇒$2x+5=0$ or, $2x-3=0$

⇒ $2x=-5$ or, $2x=3$

⇒ $x=-\dfrac{5}{2}$ or $x=\dfrac{3}{2}$

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