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Lesson · Grade 11 · Pre Calculus

Simplifying Rational Expressions and Their Non-Permissible Values

  • Grade 11
  • Pre Calculus
  • 2 min 6 s
  • British Columbia
  • BC11-MA-70

The video factors (x² − 9)/(x² + 5x + 6) into (x − 3)(x + 3)/((x + 2)(x + 3)), finds the non-permissible values x ≠ −2 and x ≠ −3 before cancelling, and simplifies to (x − 3)/(x + 2). It shows why x ≠ −3 stays even after x + 3 cancels, checks the answer at x = 1, shows that crossing out the x² terms gives a wrong result, and ends with the same steps for multiplying and dividing and a one-line recap.

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In one sentence

The question this lesson answers

How do we simplify x squared minus 9, over x squared plus 5x plus 6?

This is a rational expression: one polynomial divided by another. Any x that makes the denominator zero is a non-permissible value.

Transcript

What the lesson says

How do we simplify x squared minus 9, over x squared plus 5x plus 6?

This is a rational expression: one polynomial divided by another. Any x that makes the denominator zero is a non-permissible value.

First, factor. The top, x squared minus 9, is a difference of squares: x minus 3, times x plus 3.

For the bottom, find two numbers that multiply to 6 and add to 5: 2 and 3.

So the bottom is x plus 2, times x plus 3.

Before cancelling, set each factor of the denominator equal to zero.

x plus 2 is zero when x is negative 2, and x plus 3 is zero when x is negative 3.

Now cancel the common factor, x plus 3, from the top and the bottom.

What is left is x minus 3, over x plus 2.

Keep x not equal to negative 3, even though x plus 3 is gone.

At negative 3, the original denominator is 9 minus 15 plus 6, which is zero.

Check with x equals 1. The original gives negative 8 over 12, or negative two thirds.

The simplified form gives negative 2 over 3. They match.

Do not cross out the x squared. It is a term, added or subtracted, not a factor, which is multiplied.

At x equals 1, that would give negative 9 over 11, not negative two thirds.

Multiplying and dividing work the same way: factor, flip any divisor, find the non-permissible values before and after the flip, then cancel.

So: factor first, find the non-permissible values, then cancel only common factors.

Curriculum

Where this fits

British Columbia, Grade 11

Pre Calculus 11, Algebra: rational expressions and equationsBC11-MA-70

Previous: Factoring Trinomials by DecompositionNext: Adding and Subtracting Rational Expressions

The outcomes and strands follow the British Columbia curriculum.

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