Question

x/x+1 + x+1/x = 34/15​

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER

Given:

• x/(x + 1) + (x + 1)/x = 34/15

To Find:

• Value of x

Solution:

We are given that,

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

Now, we will take LCM at LHS,

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

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

We know that,

⇒ (a + b)² = a² + b² + 2ab

So,

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

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

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

On cross-multiplying,

$\implies15(2x^2+2x+1)=34(x^2+x)$

$\implies30x^2+30x+15=34x^2+34x$

Transposing LHS to RHS,

$\implies0=34x^2+34x-(30x^2+30x+15)$

$\implies0=34x^2+34x-30x^2-30x-15$

So,

$\implies4x^2+4x-15=0$

On splitting the middle term,

$\implies4x^2+10x-6x-15=0$

$\implies2x(2x+5)-3(2x+5)=0$

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

So,

$\implies2x+5=0\:\:\&\:\:2x-3=0$

$\implies2x=-5\:\:\&\:\:2x=3$

Hence,

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

Therefore, the value of x is -5/2(or -2.5) and 3/2(or 1.5).