rational expressions

Pre-Calculus 11 Week 15 – Solving Rational Equations

alexr2015

This week, we solved rational equations

Note that this is different from last week, where we only simplified rational expressions.

Simplifying looks like this:

\frac {x^2+5x+6}{x+3}

 

\frac {(x+2)(x+3)}{x+3}

 

x+2

And solving looks like this:

\frac {x^2+5x+6}{x+3}=

 

\frac {(x+2)(x+3)}{x+3}

 

x+2

 

x = -2

 

The major difference here is the equal sign that is present when solving vs no equal sign when simplifying.

A common issue with solving ration expressions is how to add together two or more fractions when they have different denominators. Simply remove the denominator like so

\frac {x-1}{x-3}= \frac{x+1}{x-4}

 

\frac {(x-1)(x-3)(x-4)}{x-3} = \frac {(x+1)(x-3)(x-4)}{x-4}

 

x^2-4x-3 = x^2-2x-3

 

= 0=3x-7

 

3x=7

 

x = \frac {3}{7}

Pre-Calculus 11 Week 14 – Simplifying Rational Expressions

alexr2015

This week, we started a new unit. This unit is on rational expressions.

A rational expression you might find in grade 11 is \frac{(x+2)(x+3}{(x+2)(x-2)}

To simplify this expression, we find anything common between the numerator and denominator. In this case, the binomial (x+2) exists in the numerator and denominator. So we can cross it out, and our final answer is \frac{(x+3)}{(x-2)}

What if you had quadratics as your numerator and denominator like \frac{x^2+x-6}{(x-2)}

Well, we can factor the quadratic into (x+3) and (x-2). What do you see now? Now our rational expression can be simplified!

\frac{(x+3)(x-2)}{(x-2}

 

(x+3)

 

However, if you have a rational expression like \frac {x+3}{x+2}, remember that this cannot be simplified any further. This is it’s final form! You cannot take away the x from the numerator and denominator, as tempting as it is. If you follow through with it, your answers will be wrong. So beware!