7. Solve for x and check.

 

This is a rational equation, so we run through the steps for solving rational equations. First clear denominators. In this case the smallest common denominator is (x-1)(x+5).When we multiply both sides

 

 

we get

 

 

which amounts to cross multiplying

 

 

Remove parentheses

 

 

Transpose known terms to one side and unknown terms to the other

 

 

Combine

 

 

Divide both sides by the coefficient of the unknown.

 

 

 

Check

 

Copy down the original equation

 

 

except that wherever you see an x, copy down the solution in parentheses.

 

 

This gives us compound fractions. We simplify both of them. First do the additions and subtractions on both of the bottoms. For this we will need common denominators. Multiply and divide the number terms in the bottoms by 5.

 

 

Now that we have common denominators we can add and subtract on the bottoms.

 

 

or

 

 

We are now ready to invert and multiply.

 

 

or

 

 

which checks.

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