We have,
(7x – 2) / (5x – 1) = (7x +3)/(5x + 4)
(7x – 2) / (5x – 1) – (7x +3)/(5x + 4) = 0
By taking LCM as (5x – 1) (5x + 4)
((7x-2) (5x+4) – (7x+3)(5x-1)) / (5x – 1) (5x + 4) = 0
By cross-multiplying we get,
(7x-2) (5x+4) – (7x+3)(5x-1) = 0
Upon simplification,
35x2 + 28x – 10x – 8 – 35x2 + 7x – 15x + 3 = 0
10x – 5 = 0
10x = 5
x = 5/10
= 1/2
Now let us verify the given equation,
(7x – 2) / (5x – 1) = (7x +3)/(5x + 4)
By substituting the value of ‘x’ we get,
(7(1/2) – 2) / (5(1/2) – 1) = (7(1/2) + 3) /(5(1/2) + 4)
(7/2 – 2) / (5/2 – 1) = (7/2 + 3) / (5/2 + 4)
((7-4)/2) / ((5-2)/2) = ((7+6)/2) / ((5+8)/2)
(3/2) / (3/2) = (13/2) / (13/2)
1 = 1
Hence, the given equation is verified.
