Week 15 – Pre-calculus

This week in Math 11 we learned about we learned how to add and subtract rational expressions that have binomial along with trinomial denominators. To do this we have to first simplify each rational expression. Then find the lowest common denominator between the rational expressions you are add or subtracting, once you find the LCD make sure you multiply the numerator by what you multiplied to get the LCD. Then put the numerators of both rational expressions over the LCD. What you do from here is solve. Once you finish solving you reduce if you can and make sure you don’t forget to write your non-permissible values.

Example:

$\frac{x - 2}{x^2 - 5x + 6}$ – $\frac{x + 4}{x^2 - 11x +30}$

First thing we do is simplify

$\frac{x - 2}{x^2 - 5x + 6}$ – $\frac{x + 4}{x^2 - 11x +30}$

$\frac{x - 2}{(x - 2)(x - 3)}$ – $\frac{x + 4}{(x - 5)(x - 6)}$

now that we have simplified our expressions we can also write our non-permissible values.

$x \neq 2, 3, 5, 6$

also note that you can simplify as long as it’s within the same expression.

$\frac{x - 2}{(x - 2)(x - 3)}$ – $\frac{x + 4}{(x - 5)(x - 6)}$

here we can simplify the (x – 2) because it is within the same fraction

$\frac{1}{(x - 3)}$ – $\frac{x + 4}{(x - 5)(x - 6)}$

now we find our LCD which is (x – 3)(x – 5)(x – 6)
and whatever we multiplied the bottom by we have to multiply the top by

$\frac{(x - 5)(x - 6) - (x + 4)(x - 3)}{(x - 3)(x - 5)(x - 6)}$

Now we can solve the numerator

$\frac{x^2 - 11x + 30 - (x^2 + x - 12)}{(x - 3)(x - 5)(x - 6)}$ $\frac{x^2 - 11x + 30 - x^2 - x + 12)}{(x - 3)(x - 5)(x - 6)}$ $\frac{-12x + 42}{(x - 3)(x - 5)(x - 6)}$

and we can see that we can factor out a -6 in our numerator

$\frac{-6(2n - 7)}{(x - 3)(x - 5)(x - 6)}$

so our final answer would be

$\frac{-6(2n - 7)}{(x - 3)(x - 5)(x - 6)}$ $x \neq 2, 3, 5, 6$

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Week 15 – Pre-calculus

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