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Polynomial expressions

How do you solve these?

1) Find all numbers that are undefined for the expression,

x^2 - 3x -54 divided by x^2 - 10x + 24

2) Simplify x^2 - 4x - 32 divided by x^2 - 64

3) Perform the indicated operation

(x^2 + 16)/ (x^2 - 16) divided by (x + 4)/(x^2 + 2x - 8)

4) Simplify

1/x + 1/y divided by 1/x - 1/y

5) Solve

2/x - 5 = 2/x

Solution Preview

1) Find all numbers that are undefined for the expression,

x^2 - 3x -54 divided by x^2 - 10x + 24

Solution. All numbers that are undefined for the expression are those such that

x^2 - 10x + 24=0

i.e.,
(x-4)(x-6)=0

So, x=4 or x=6

Hence, all numbers that are undefined for the above expression are 4 and 6.

2) Simplify x^2 - 4x - 32 divided ...

Solution Summary

This shows how to work with polynomials, including solving equations, division, and finding the numbers at which the expression is undefined.

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