How do you solve #x/5 - 4/5 = 1/x #?

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Answer 1 · 2015-12-15T19:59:52

#x=5# and #x=-1#

Original Equation:
#x/5-4/5=1/x#

First, subtract the two fractions on the left:
#(x-4)/5=1/x#

Next, cross multiply:
#x(x-4)=5#

Multiply the left out:
#x^2-4x=5#

Bring the #5# over:
#x^2-4x-5=0#

Factor:
#(x-5)(x+1)=0#

Solve:
#x=5# and #x=-1#