Specify any values that must be excluded from the solution set and then solve the equation. (1)/

Specify any values that must be excluded from the solution...

Key Concepts

Clearing Fractions

Clearing fractions involves multiplying both sides of an equation by the least common denominator to eliminate the fractions. This process transforms a rational equation into a polynomial equation, which is typically easier to solve, while being careful not to introduce extraneous solutions.

Domain Restrictions

Domain restrictions are the conditions that arise from the fact that denominators in rational expressions cannot be zero. Before solving rational equations, it is essential to identify and exclude any values that would make a denominator equal to zero, as these lead to undefined expressions.

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. They are analyzed by ensuring that the expressions are defined, which means the denominator should not equal zero. Understanding rational expressions is crucial when solving equations that involve them.

Common Denominator

Finding a common denominator involves rewriting multiple rational expressions so they share the same denominator. This technique allows for the combination or comparison of fractions and is a key step in simplifying and solving rational equations.

Transcript

00:01 For this problem, you can use the least common denominators in combining like terms to solve for c.

00:07 To start, let's see if there's any exclusions from c because they are all in the denominator.

00:13 So for the 1 over c minus 2, that cannot equal 0.

00:17 So we're going to do c minus 2 cannot equal 0 and solve for c.

00:24 So if we add 2 to both sides, c cannot equal positive 2.

00:29 So we will keep this in mind when solving for our answer.

00:34 And then the 1 over c means that c cannot equal 0 because it is the only thing in the denominator.

00:41 So these two will be excluded from our answers.

00:48 To start this problem, we will want to get the same denominators for each part.

00:54 So on the very left side, the 1 over c minus 2 can be multiplied by c over c to get the same denominators.

01:02 Denominators.

01:05 On the 1 over c, we can multiply that by c minus 2 over c minus 2.

01:19 So this will equal out to being c over c minus 2 plus c minus 2 over c times c minus 2.

01:46 And on the right side of this equation, it will be the same since it is already in the least common denominator.

01:54 So it will be 2 over c times c minus 2.

02:00 Now that they are all in the same denominators, we are able to get it to one side of the equation to be able to solve for c.

02:08 For this, i am going to subtract the 2 over c times c minus 2 to be able to solve.

02:18 So when this is subtracted, the new equation will equal c over c times c minus 2 plus c minus 2 over c times c minus 2...

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