Question

9/x+2=x+3/x-5 Can someone solve for me with steps?

Answer 1

$\\ \tt\longmapsto \dfrac{9}{x+2}=\dfrac{x+3}{x-5}$

$\\ \tt\longmapsto 9(x-5)=(x+2)(x+3)$

$\\ \tt\longmapsto 9x-45=x^2+5x+6$

$\\ \tt\longmapsto x^2-4x+51=0$

• a=1
• b=-4
• c=51

Let's find x

$\\ \tt\hookrightarrow x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\\ \tt\hookrightarrow x=\dfrac{4\pm\sqrt{16-204}}{2}$

$\\ \tt\hookrightarrow x=\dfrac{4\pm \sqrt{-188}}{2}$

$\\ \tt\hookrightarrow x=\dfrac{4\pm \sqrt{188}i}{2}$

• i=√-1

$\\ \tt\hookrightarrow x=\dfrac{4\pm 2\sqrt{47}i}{2}$

$\\ \tt\hookrightarrow x=2\pm \sqrt{47}i$

Answer 2

$\frac{9}{x + 2} = \frac{x + 3}{x - 5}$

Simplify the equation using cross-multiplication

$9(x - 5) = (x + 3)(x + 2)$

Move the expression to the left-hand side and change its sign

$9(x - 5) - (x + 3)(x + 2) = 0$

Distribute 9 through the parentheses and multiply the parentheses

$9x - 45 - (x + 3)(x + 2) = 0$

$9x - 45 - (x ^{2} + 2x + 3x + 6) = 0$

Collect like terms

$9x - 45 - ( {x}^{2} + 5x + 6) = 0$

When there is a - in front of an expression in parentheses, change the sign of each term in the expression

$9x - 45 - {x}^{2} - 5x - 6 = 0$

Collect like terms

$4x - 45 - {x}^{2} - 6 = 0$

Calculate the difference

$4x - 51 - {x}^{2} = 0$

Use commutative property to reorder the terms

${x}^{2} - 4x +51 = 0$