How do you solve #\frac { 3} { x + 2} + \frac { 7} { x } = \frac { 8} { x ^ { 2} + 2x }#?

1 Answer
Shell
Dec 9, 2016

#x=-3/5#

Explanation:

#3/(x+2) +7/x= 8/(x^2+2x)#

Factor out the GCF #x# from the denominator in the term on the right.

#3/(x+2) +7/x= 8/(x(x+2))#

Get a common denominator.

#x/x * 3/(x+2)+ ((x+2))/((x+2)) * 7/x = 8/(x(x+2))#

Now that all the denominator are the same, they can be "removed" from the equation and it can be solved using just the numerators.

#3x +7(x+2)=8#

#3x+7x+14=8#

#10x+14=color(white)(aa)8#
#color(white)(aaa)-14color(white)(a^2)-14#

#10x=-6#

#(10x)/10=( -6)/10#

#x= -3/5#

Note that solutions to rational equations must be "checked" to make sure they do not result in dividing by zero. In this example, the only values of #x# that would result in a denominator of zero would be #x=0# or #x=-2#, so #x= -3/5# is valid.

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