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

Answer 1

Isaiah Anthony

#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"#

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Answer 2

Genesis Allen

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 #

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Answer 3

Eva Adamson

To solve ( \frac{4}{x + 3} = \frac{2}{x - 3} ), cross-multiply to eliminate the denominators. Then, solve for ( x ).

[ 4(x - 3) = 2(x + 3) ]

[ 4x - 12 = 2x + 6 ]

[ 4x - 2x = 12 + 6 ]

[ 2x = 18 ]

[ x = 9 ]

So, the solution to the equation is ( x = 9 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.