IXL - Solve rational equations (Precalculus practice)

Solve for d.

d − 5

d − 6

There may be 1 or 2 solutions.

d = or d =

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question

Solve for c.

c + 9

There may be 1 or 2 solutions.

c = or c =

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 c.

c + 9

Multiply both sides by c(c + 9)

2[c(c + 9)]

5[c(c + 9)]

c + 9

Multiply both sides by c(c + 9)

Simplify

2(c + 9)

Simplify

Apply the distributive property

2c + 18

Apply the distributive property

Subtract 2c from both sides

Divide both sides by 3

Now check whether this is an extraneous solution. Plugging c = 6 into the first denominator, c, yields 6. Plugging c = 6 into the second denominator, c + 9, yields 15. Since neither denominator is 0, which would be undefined, this is a valid solution.

The
solution
is
c
= 6
.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

B.1Solve linear equations

L.3Multiply polynomials

D.6Solve a quadratic equation by factoring

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