Question

2/x-1+3/x+4=5/x+3solve for x​

Answer 1

ANSWER:

$\frac{2}{x - 1} + \frac{3}{x + 4} = \frac{5}{x + 3}$

$\frac{2(x + 4) + 3(x - 1)}{(x - 1)(x + 4)} = \frac{5}{x + 3}$

$\frac{2x + 8 + 3x - 3}{x(x + 4) - 1(x + 4)} = \frac{5}{x + 3}$

$\frac{5x + 5}{ {x}^{2} + 4x - x - 4 } = \frac{5}{x + 3}$

$\frac{5x + 5}{ {x}^{2} + 3x - 4} = \frac{5}{x + 3}$

$cross \: \: multiplication$

$(5x + 5)(x + 3) = 5( {x}^{2} + 3x - 4)$

$5x(x + 3) + 5(x + 3) = 5 {x}^{2} + 15x - 20$

$5 {x}^{2} + 15x + 5x + 15 = 5 {x}^{2} + 15x - 20$

$5 {x}^{2} + 20x + 15 = 5 {x}^{2} + 15x - 20$

$5( {x}^{2} + 4x + 3) = 5( {x}^{2} + 3x - 4)$

${x}^{2} + 4x + 3 = {x}^{2} + 3x - 4$

${x}^{2} - {x}^{2} + 4x - 3x = - 4 - 3$

$4x - 3x = - 4 - 3$

$x = - 7$

CHECK:

$\frac{2}{x - 1} + \frac{3}{x + 4} = \frac{5}{x + 3}$

$\frac{2}{ - 7- 1} + \frac{3}{ - 7+ 4} = \frac{5}{ - 7+ 3}$

$\frac{2}{ - 8} + \frac{3}{ - 3} = \frac{5}{ - 4}$

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

$- \frac{1}{4} - 1 = - \frac{5}{4}$

$\frac{ - 1 - 4}{4} = \frac{ - 5}{4}$

$\frac{ - 5}{4} = \frac{ - 5}{4}$

$- 1.25 = - 1.25$

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