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

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

Key Concepts

Rational Equations

A rational equation is an equation that involves one or more rational expressions, which are fractions that contain polynomials in the numerator and denominator. Solving rational equations typically involves finding a common denominator, clearing the fractions, and then solving the resulting equation.

Domain Restrictions

Domain restrictions refer to the values that make any denominator equal to zero, because division by zero is undefined. When solving rational equations, it's vital to determine these critical values and exclude them from the solution set to ensure the solutions are valid.

Clearing Fractions

Clearing fractions involves eliminating the denominators by multiplying both sides of the equation by a common denominator, which simplifies the equation by converting it into a polynomial equation. This step is essential to avoid dealing directly with fractions when solving the equation.

Solving Linear Equations

After clearing the fractions in a rational equation, the result is often a linear or polynomial equation that can be solved using standard algebraic methods. These methods include combining like terms, isolating the variable, and solving for its value.

Transcript

00:01 For this problem, to be able to solve for n, you will need to use the least common denominators in combining like terms.

00:07 To start, we notice that there are ends in the denominator.

00:12 So we need to see if there's any exclusions.

00:16 So it'll be 6n minus 6 cannot equal 0.

00:21 And this will be the same as 4 since they both have the same whole numbers.

00:29 So if we add six onto both sides, it will be 6n equals 6.

00:39 Divide both sides by 6, and n cannot equal 1.

00:48 So we will keep this in mind when solving.

00:53 And this will be the same for 4 because if we added 4, it would be 4 over 4, which equals 1.

01:00 To start this problem, we will need to get the same common denominators.

01:06 For this, we have a six in the denominator on the left side of the equation and a four on the right.

01:12 So we know that the least common denominator will be 12.

01:16 So on the left side, we will multiply this times two.

01:23 And on the right side, we can multiply this by three.

01:29 So this will equal 2n minus 5 over, which equals 1 9th minus 3 n minus 3 over 12n.

02:25 Now that we have the same denominators, we are able to put them onto one side of the equation.

02:31 So i'm going to add the 3 times n minus 3 to the left side of the equation.

02:50 And there should be an n in this right here in the denominator.

02:59 So these will cancel out.

03:01 And the new equation will equal 2n minus 5 over 12n minus 12 plus 1.

03:24 Because we're adding this 3 and minus 3 over, which all equals 1 .9th.

03:46 The next step will be to combine the numerators.

03:51 But before we can do that, let's try and use our distributive properties to distribute our 2 and our 3.

04:02 So this will equal 2n minus 10 over our denominators, so 12n minus 12, plus distribute in the 3.

04:29 So it'll be 3n minus 9 over 12n minus 12.

04:48 So now that they are distributed and simplified, we are able to combine the numerators...

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