Question

plz solve this......asap.....​

Answer 1

Solution of the equation is x=$\frac{3}{2}$ or x = $\frac{-5}{2}$.

• Given equation is $\frac{x}{x+1}  + \frac{x+1}{x}$ =$\frac{34}{15}$.
• To solve this equation we cross multiply denominators to make the denominators equal so that we can perform addition.

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

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

• Multiplying the denominator on other side

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

$30x^{2} + 30x +15 = 34x^{2}  + 34x$

$4x^{2}  + 4x -15 = 0$

• Solving the above quadratic equation, we get

$4x^{2}  + 10x - 6x -15 = 0$

$2x(2x  + 5) -3(2x + 5) = 0$

(2x-3)(2x+5) = 0

• Therefore, 2x-3 =0 or 2x+5 =0

x = 3/2 or x = -5/2