IXL - Solve rational equations with one solution (Algebra 1 practice)

Solve for v.

^–9

v − 7

^–1

v + 1

v =

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question

Solve for q.

q + 10

^–7

q − 4

q =

key idea

To solve a rational equation, first clear the fractions, by multiplying both sides by the denominators or by the lowest common denominator (LCD). Then solve for the variable.

solution

Solve for q.

q + 10

^–7

q − 4

Multiply both sides by (q + 10)(q − 4)

7[(q + 10)(q − 4)]

q + 10

^–7[(q + 10)(q − 4)]

q − 4

Multiply both sides by (q + 10)(q − 4)

Simplify

7(q − 4)

^–7(q + 10)

Simplify

Apply the distributive property

7q − 28

^–7q − 70

Apply the distributive property

Add 7q to both sides

14q − 28

^–70

Add 7q to both sides

Add 28 to both sides

14q

^–42

Add 28 to both sides

Divide both sides by 14

^–3

Divide both sides by 14

Now check whether this is an extraneous solution. Plugging q = ^–3 into the first denominator, q + 10, yields 7. Plugging q = ^–3 into the second denominator, q − 4, yields ^–7. Since neither denominator is 0, which would be undefined, this is a valid solution.

The
solution
is
q
= ^–3
.

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Work it out

Not feeling ready yet? These can help:

C.12Solve linear equations with variables on both sides

W.8Multiply two binomials

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