Question

plz give the easiest method to solve this equation
solve for x: [tex]\frac{1}{x+1} +\frac{3}{5x+1} =\frac{5}{x+4} ,x≠-1,-1/5,-4

Answer 1

Answer:

The values of x are  1 and -11/17 .

Step-by-step explanation:

Here, the  question is -

$\frac{1}{x+1} +\frac{3}{5x +1} =\frac{5}{x+4}$

Firstly, we will take LCM on LHS .

$\frac{5x +1+3x+3}{(x+1)(5x+1)} =\frac{5}{x+4}$

$=> \frac{8x+4}{5x^{2} +6x+1} =\frac{x}{x+4}$

Than, we will do cross multiplication

=>  8x² + 36x + 16 = 25x² + 30x + 5

A quadratic equation is formed by solving it -

=>  17x² - 6x - 11 = 0

We will solve this by quadratic formula -

First, we will calculate Discriminant ,D

D = b² - 4ac

   =  (-6)² - 4*17*(-11)

   =  784

So, √D = √784

              =  28

So, values of x are given by formula -

x = (-b±√D)/2a

So,  x1  =  (6+28)/(2 * 17)

            =  1

      x2  =  (6-28)/(2 * 17)

            = (-22)/(2 * 17)   = -11/17

So, values of x are  1 and -11/17