Question

Solve : 3/3x-1 + 5/5x-1=8​

Answer 1

Answer:

$\frac{3}{3x - 1} + \frac{5}{5x - 1} = 8 \\ \\ \frac{3(5x - 1) + 5(3x - 1)}{(5x - 1)(3x - 1)} = 8 \\ \\ \frac{15x - 3 + 15x - 5}{15 {x }^{2} - 5x - 3x + 1} = 8 \\ \\ \frac{30x - 8}{15 {x}^{2} - 8x + 1} = 8 \\ \\ 8(15 {x}^{2} - 8x + 1) = 30x - 8 \\ \\ 120 {x}^{2} - 64x + 8 - 30x + 8 = 0 \\ \\ 120 {x}^{2} - 94x + 16 = 0 \\ \\ 60 {x}^{2} - 47x + 8 = 0 \\ \\ x \: = 47 + \: or \: - \frac{ \sqrt{ {47}^{2} - 4(60)( 8)} }{2(60)} \\ \\ x = 47+ \: or \: - \frac{ \sqrt{2209 - 1920} }{120} \\ \\ x = 47+ \: or \: - \: \frac{17}{120} \\ \\ x = \frac{5523}{120} \: or \: \frac{5657}{120}$

x = 46.025 or x = 47.14167

Answer 2

$\frac{3}{3x - 1} + \frac{5}{5x - 1} = 8 \\ \frac{3(5x - 1) + 5(3x - 1)}{(3x - 1)(5x - 1)} = 8 \\ \frac{15x - 3 + 15x - 5}{ {15x}^{2} - 3x - 5x + 1} = 8 \\ \frac{30x - 8}{ {15x}^{2} - 8x + 1 } = 8 \\ 8( {15x}^{2} - 8x + 1) = 30x - 8 \\ {120x}^{2} - 64x + 8 - 30x + 8 = 0 \\ 120x ^{2} - 94x^{2} + 16 = 0 \\ {60x}^{2} - 47 + 8 = 0 \\ {60x}^{2} - 32x - 15x + 8 = 0 \\ 4x(15x - 8) - 1(15x - 8) = 0 \\ (4x - 1)(15x - 8) = 0$

4x-1=0 and 15x-8=0

4x=1 ànd 15x= 8

x=1/4 ànd x= 8/15

x= 1/4 , 8/15