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 #