SOLUTION: How do you solve for x when it is in the denominator of a rational expression such as in the following: 1/8 - 3/5 = 1/x What are the restrictions? What is the solution?

Question 81622This question is from textbook Algebra 1
: How do you solve for x when it is in the denominator of a rational expression such as in the following:
1/8 - 3/5 = 1/x What are the restrictions? What is the solution? This question is from textbook Algebra 1

Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
THERE ARE NO RESTRICTIONS.
FIRST YOU MUST COMBINE ALL THE FRACTIONS BY FINDING A COMMON DENOMINATOR LIKE 40.
1/8=5*1/40=5/40 & -3/5=-3*8/40=-24/40
5/40-24/40=1/X
(5-24)/40=1/X
-19/40=1/X NOW CROSS MULTIPLY
-19X=40
X=40/-19
X=-40/19 ANSWER.
PROOF
1/8-3/5=1/(-40/19) A FRACTION IN THE DENOMINATOR (-40/19) NEEDS TO BE INVERTED AND THEN MULTIPLIED BY THE NUMERATOR THUS:
1/8-3/5=-19/40
5/40-24/40=-19/40
-19/40=-19/40
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