Question

For what value of x will 2x+1/3x-2 and 3x-4/x+8 represent the same fraction? Aslo find the fraction.​

Answer 1

Answer:

$\frac{2x+1}{3x-2}= \frac{3x - 4}{x+8}\\Cross\:multiply\\(x + 8)(2x + 1) = (3x - 4)(3x - 2) \\ x(2x + 1) + 8(2x + 1) = 3x(3x - 2) - 4(3x - 2) \\ 2 {x}^{2} + x + 16x + 8 = 9 {x}^{2} - 6x - 12x + 8 \\ 2 {x}^{2} + 17x + 8 = 9 {x}^{2} - 18x + 8 \\ 2 {x}^{2} - 9 {x}^{2} + 17x + 18x + 8 - 8 = 0 \\ ( - 7 {x}^{2} ) + 35x = 0 \\ ( - 7 {x}^{2} ) = ( - 35x) \\ 7 {x}^{2} = 35x \\ 7x = 35 \\ x = \frac{35}{7} \\ x = 5 \\ \frac{2x + 1}{3 x- 2} = \frac{2(5) + 1}{3(5) - 2} = \frac{10 + 1}{15 - 2} = \frac{11}{13} \\ \frac{3x - 4}{x + 8} = \frac{3(5) - 4}{5 + 8} = \frac{15 - 4}{5 + 8} = \frac{11}{13} \\ Therefore, \: the \: fractions \: are \: \frac{11}{13} \: and \: \frac{11}{13} .$