Specify any values that must be excluded from the solution set and then solve the equation. (5)/

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

Key Concepts

Excluded Values/Domain Restrictions

In equations involving rational expressions, it is essential to determine the values that make any denominator zero. These values are excluded from the solution set because they would cause the expression to be undefined. For instance, if a variable appears in a denominator, setting the denominator equal to zero identifies values that must be excluded.

Least Common Denominator (LCD) and Clearing Fractions

A common strategy for solving rational equations is to multiply both sides of the equation by the least common denominator (LCD) of all fractional expressions. This step eliminates the denominators and transforms the rational equation into a polynomial or linear equation that is easier to solve.

Solving Resulting Equations

After clearing the fractions, the equation simplifies to a more straightforward form. The next step is to solve this resulting equation using appropriate algebraic techniques such as combining like terms and isolating the variable.

Transcript

00:01 For this problem, to be able to suffer in, you can use the least common denominator in combining like terms.

00:06 To start, we need to see if there's any exclusions to our variables since they are in the denominator.

00:13 So if we have 5 over m, we know that m cannot equal 0 because it is the only thing in the denominator.

00:21 So this will be excluded from our answers.

00:24 And the next one is 3 over m minus 2.

00:27 So we'll set that equal to zero to see what m will solve.

00:32 So if we add two to both sides, m cannot equal positive 2.

00:38 So both of these will be excluded from our answers.

00:43 To start solving this, we need to get the same denominators.

00:47 So i'm going to multiply m minus 2 over m minus 2 by 5 over m.

00:55 So this will give us our least common denominator.

01:02 For our 3 over m minus 2, we can multiply that by m over m.

01:16 So this will equal, we need to multiply and distribute 5m minus 10 over m times n minus 2.

01:40 And this will be added to 3m over m times m minus 2.

01:56 And on the right side of the equation, it will be the same since it already has the least common denominator.

02:03 So it will be 6 over m times m minus 2.

02:11 Now that they are all in the same denominators, we are able to bring them all to one side of the problem to be able to get the numerators combined.

02:20 So i am going to subtract the right side of the equation and bring it over.

02:32 And this will cancel out to zero on the right side and then be subtracted to the left...

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