How do you solve #\frac { 8} { x - 2} + 3= \frac { x + 6} { x - 2}#?

1 Answer
Meave60
Jun 25, 2018

There is no solution.

Explanation:

Solve:

#8/(x-2)+3=(x+6)/(x-2)#

Multiply both sides by the least common denominator #(x-2)#.

#(x-2)xx(8)/(x-2)+(x-2)xx3=(x+6)/(x-2)xx(x-2)#

Simplify.

#color(red)cancel(color(black)((x-2)))^1xx(8)/color(red)cancel(color(black)((x-2)))^1+(x-2)xx3=(x+6)/color(red)cancel(color(black)((x-2)))^1xxcolor(red)cancel(color(black)((x-2)))^1#

#8+3(x-2)=x+6#

Expand.

#8+3x-6=x+6#

Simplify.

#3x+2=x+6#

Subtract #x# from both sides.

#3x-x+2=6#

Simplify.

#2x+2=6#

Subtract #2# from both sides.

#2x=6-2#

Simplify.

#2x=4#

Divide both sides by #2#.

#x=4/2#

Reduce.

#x=2#

Check

#8/(x-2)+3=(x+6)/(x-2)#

Substitute #2# for #x#.

#8/(2-2)+3=(2+6)/(2-2)#

#8/0+3=8/0#

#n/0# is undefined, and both sides are not equal, so there is no solution.

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