Algebra Review

A few basic facts you will need to remember

but and are undefined

and does not factor for example do not factor.

always has one real solution whether a is positive or negative.

,

Quadratic Formula: The solution(s) to are and

Exponents: for x not 0, ,

,

,

Cancellation: Only cancel common factors, not summands.

Ex.

x is not a factor of the numerator and cannot be cancelled.

x + 2 is not a factor of the denominator and cannot be cancelled.

for

Miscellaneous problems you will see again in similar form:

Collect terms and factor . Each summand contains so we can factor it out. This leaves =

Practice problem: Solve

solution

Rationalize the numerator of . To do this multiply by 1 in the form . .

Notice that the original expression was undefined at h=0 but the last expression is defined at h=0.

Solve Put it over a common denominator. To do this multiply by 1 in the form of . This leaves which is 0 at Both are between -1 and 1 where the expressions are defined.