Week 13 Pre Calc 11 – Adam’s Blog

This week in Pre Calc 11, I learned how to add and subtract Rational Expressions. This week we mainly focused on adding and subtracting rational expressions and a bit of equations. In this, I will be talking about adding and subtracting rational expressions, as well as solving rational expressions.

First, you have to make a common denominator, then simplify from there.

Let’s try a simple question:

$\frac{5}{3x^2}$ + $\frac{x}{2}$

So in this question, we need to find a common denominator. The common denominator for this question would be $6x^2$ . So we need to multiply $\frac{5}{3x^2}$ by 2, and we need to multiply $\frac{x}{2}$ by $3x^2$ . This will equal $\frac{10}{6x^2}$ + $\frac{3x^3}{6x^2}$ . From here we can get rid of the fraction and just have $10 + 3x^3$ . Now all we have to do in this question is simplify, so we do not have to go any further.

Now, let’s try a harder question:

$\frac{2x}{x+3}$ + $\frac{3x}{2x + 8}$ ÷ $\frac{x^2}{3x +12}$

$\frac{2x}{x+3}$ + $\frac{3x}{2(x + 4)}$ x $\frac{3(x+4)}{x^2}$

So, we can cancel out the x+4 and we can cancel the x out too. So this comes out $\frac{2x}{x+3}$ + $\frac{3}{2}$ multiplied by $\frac{3}{x}$

From here we can use bedmas and simplify this equation we can multiply and this comes out to $\frac{2x}{x+3}$ + $\frac{9}{2x}$

At this point we need to find a common denominator to further simplify this. The common denominator that we will use is 2x(x+3). So we need to multiply 2x by 2x, and we need to multiply 9 by (x+3). This comes out to $\frac{4x^2 + 9x +27}{2x (x+3)}$ . This is the final solution to this question.