How do you solve #\frac { x + 5} { x + 4} + 1= \frac { 1} { x + 4}#?

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Answer 1 · 2017-07-11T02:20:47

#x=-4#

#(x+5)/(x+4)+1=1/(x+4)#

Multiply all terms by #(x+4)# to remove fractions.

#((x+4)xx(x+5)/(x+4))+1(x+4)=(x+4)xx1/(x+4)#

#(1cancel((x+4))xx(x+5)/(1cancel((x+4))))+x+4=1cancel((x+4))xx1/(1cancel((x+4)))#

#x+5+x+4=1#

#2x+9=1#

Subtract #9# from each side.

#2x+9-9=1-9#

#2x=-8#

Divide both sides by #2#.

#(2x)/2=(-8)/2#

#(1cancel2x)/(1cancel2)=(-4cancel8)/(1cancel2)#

#x=-4#