Question

Which expression is in simplified form for the given expression and states the correct variable restriction?

u^2-4/(u-6)(u-2)
a. 1/u-3, u=3
b. u+2/u-6, u=2, u=6
c. 1/2u+12, u=-6
d. u+2/u-6, u=6

Answer 1

(u^2 - 4) / (u-6)(u-2)

Resriction u ≠ 6 and u ≠ 2 (because the denominator cannot be equal lto zero)

Simplification

u^2 - 4 is a difference of two squares, then you can factor it as the product of (u+2)(u-2). So, you can write the expression as:

(u+2)(u-2) / (u-2)(u-6)

Simplify u -2 (because it appears in the numerator and the denominator)

(u + 2) / (u -6), with u ≠2 and u≠6