Homework

Problem 1 · easy

Find the domain of (x - 3)/(x + 5). Exclude which x-value?

Problem 2 · easy

Find the excluded values of (2x)/(x^2 - 9).

Problem 3 · easy

Simplify: (x^2 - 4)/(x - 2)

Problem 4 · easy

Simplify: (3x^2 + 6x)/(9x)

Problem 5 · medium

Simplify: (x^2 + 7x + 12)/(x^2 + 5x + 4)

Problem 6 · medium

Multiply: (x+1)/(x-2) * (x^2-4)/(x+1)^2

Problem 7 · medium

Multiply: (x^2-9)/(x+4) * (x^2+8x+16)/(x-3)

Problem 8 · medium

Divide: (x^2-1)/(x+3) / (x-1)/(x+3)

Problem 9 · medium

Divide: (2x^2 + 4x)/(3) / (x + 2)/(6)

Problem 10 · easy

Add: 5/(x+3) + 2/(x+3)

Problem 11 · easy

Subtract: (3x + 1)/(x - 4) - (x - 3)/(x - 4)

Problem 12 · easy

Find the LCD of 1/(x) and 1/(x + 2).

Problem 13 · medium

Add: 2/x + 3/(x+4). Leave in simplified form.

Problem 14 · medium

Subtract: 4/(x-1) - 2/(x+2)

Problem 15 · medium

Solve: x/3 + x/4 = 7

Problem 16 · medium

Solve: 5/(x-2) = 10/x

Problem 17 · challenge

Solve and check for extraneous: 3/(x-1) + 1 = 4/(x-1)

Problem 18 · medium

Pipe A fills a pool in 8 hours. Pipe B fills it in 12 hours. How long do both together take?

Problem 19 · medium

One person can paint a room in 6 hours. Another takes 3 hours. How long together?

Problem 20 · challenge

Simplify the complex fraction: (1/2 + 1/x) / (1/2 - 1/x)

Problem 21 · challenge

Simplify: (6x^2 - 6)/(3x^2 + 3x - 6)

Problem 22 · challenge

Add: 1/(x^2-1) + 1/(x-1). Simplify.

Problem 23 · medium

Solve: 2/(x+3) - 1/(x-3) = 0

Problem 24 · challenge

Subtract: x/(x^2-4) - 2/(x-2)

Problem 25 · challenge

A car travels 120 miles. A second car travels 180 miles at 15 mph faster. Both take the same time. Find the first car's speed.