Question

solve : (7x+1)/(7x+5)= (3x+1)/(5x+1)

Answer 1

The roots of x=1and -2/7

Refer the attachments

Answer 2

Given:

(7x+1)/(7x+5)= (3x+1)/(5x+1)

To find:

We have to find the value of x.

Solution:

To determine the value of x we have to follow the below steps as follows-

The given expression is (7x+1)/(7x+5)= (3x+1)/(5x+1).

Cross multiplying the terms we get-

$\frac{7x + 1}{7x + 5} = \frac{3x + 1}{5x + 1} \\ (7x + 1)(5x + 1) = (3x + 1)(7x + 5) \\ 35 {x}^{2} + 12x + 1 = 21 {x}^{2} + 22x + 5 \\ 35 {x}^{2} - 21 {x}^{2} + 12x - 22x + 1 - 5 = 0 \\ 14 {x}^{2} - 10x - 4 = 0 \\ 7 {x}^{2} - 5x - 2 = 0 \\ 7 {x}^{2} - 7x + 2x - 2 = 0 \\ 7x(x - 1) + 2(x - 1) = 0 \\ (x - 1)(7x + 2) = 0 \\ x = 1 \\ x = \frac{ - 2}{7}$

Thus, the value of x is 1 or -2/7.