How do you solve $\frac { 4} { x + 3} = \frac { 2} { x - 3}$ ?

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Answer 1 · 2018-08-05T02:27:51

$color(violet)(x = 9$

$4 / (x = 3) = 2 / (x - 3)$

$4(x - 3) = 2 (x + 3), "cross multiplying"$

$4x - 12 = 2x + 6, " removing braces"$

$4x - 2x = 6 + 12, " bringing like terms together"$

$2x = 18 " or "x = 9, " simplifying"$

Answer 2 · 2018-08-05T02:30:38

Work backwards to isolate x

First remove the parenthesis represented by the division signs

$( x +3) xx ( x -3) xx 4/(x+3) = ( x+3) xx ( x -3) xx 2/( x-3)$

This gives

$(x -3) xx 4 = (x +3 )xx 2$

multiplying across the parenthesis using the distributive property

$4x -12 = 2x + 6$

Next adding the opposites looks like this

$4x -12 + 12 - 2x = 2x -2x + 12 + 6$

Which gives

$2x = 18$

divide both sides by 2

$2x/2 = 18/2$

$x = 9$

How do you solve \frac { 4} { x + 3} = \frac { 2} { x - 3}\frac { 4} { x + 3} = \frac { 2} { x - 3}?