How do you solve $1/(x+4)-2=(3x-2)/(x+4)$ ?

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Answer 1 · 2016-11-13T00:18:08

$x=-1$

$1/(x+4) -2 = (3x-2)/(x+4)$

Get a common denominator by multiplying the 2nd term by $(x+4)/(x+4)$

$1/(x+4)-(2 * (x+4))/((x+4))= (3x-2)/(x+4)$

$1/(x+4)- ((2x+8))/(x+4)=(3x-2)/(x+4)$

Compare to a simple equation like $1/5 + 2/5 =x/5$
Because there is a common denominator, this can be solve with the numerators only $1 +2 =x$

Similarly, solve the equation using only the numerators.

$1-(2x+8)=3x-2$

Distribute the negative.

$1-2x-8=3x-2$

$-2x-7=color(white)(aa)3x-2$
$+2x+2=+2x+2$

$-5=5x$

$-5/5 =(5x)/5$

$-1=x$

When solving rational equations, it is important to check for extraneous solutions (solutions that "don't work" or result in division by zero).

$1/(-1+4)-2=frac{3(-1)-2}{-1+4}color(white)(aaa)$ True

How do you solve 1/(x+4)-2=(3x-2)/(x+4)1/(x+4)-2=(3x-2)/(x+4)?