Rational Expression

[Softballgrl]

Hi,
I changed schools recently and I can't seem to get caught up, even after talking to my teacher. Anyways, I don't understand simplifying rational expressions
such as:
q^2+2q-3/q-1

or...q^2+2q-2 ALL OVER q-1

Mostly I don't understand how to factor these types of equations

Thanks

 

[wjm11]

Softballgrl said, "I don't understand simplifying rational expressions
such as:
q^2+2q-3/q-1

or...q^2+2q-2 ALL OVER q-1

Mostly I don't understand how to factor these types of equations"


To simplify, both the numerator and denominator must first be in factored form. In this case, the numerator must be factored:

q^2+2q-3 = (q + 3)(q – 1)

The rational expression then becomes

(q + 3)(q – 1)/(q – 1)

which simplifies to (q + 3).

For tips on factoring quadratics, try the following:

http://www.purplemath.com/modules/factquad.htm
or
http://www.wikihow.com/Factor-Second-De ... -Equations)

 

[fasteddie65]

(q^2 + 2q - 3)/(q - 1)

You need to add parentheses for clarity if you are going to write fractions horizontally.

As far as factoring, I find the best method to be something called the Product-Sum Method.

In the case of the trinomial q^2 + 2q - 3, you want factors of -3 (the constant term) whose sum is 2 (the middle term coefficient). By the way, if there is a coefficient of the quadratic term, you will need to multiply it by the constant term first.

Anyway, the factors of -3 are 1 and -3, or -1 and 3. The two factors whose sum is 2 are 3 and -1, so the factors of the trinomial are q + 3 and q - 1.