Algebra methods

Simplify a rational expression

Simplify the expression, and state the values of x for which it is not defined.

(x² − 7x + 10)/(5x − 25)x² − 7x + 105x − 25

Add two rational expressions

Write as one fraction, and state the values of x for which the expression is not defined.

5/(x + 5) + 2/(x − 4)5x + 5 + 2x − 4

Subtract two rational expressions

Write as one fraction, and state the values of x for which the expression is not defined.

1/(x + 3) − 5/(x + 4)1x + 3 − 5x + 4

Solve a rational equation

Solve the equation.

4/(x − 1) = 2/(x + 4)4x − 1 = 2x + 4

A root equation, and the false root

Solve the equation, and check every root you find.

√(−2x + 19) = x − 2√(−2x + 19) = x − 2

Isolate the root, then solve

Solve the equation, and check every root you find.

√(5x + 19) + 2 = x + 3√(5x + 19) + 2 = x + 3

From inequality to interval

Write the inequality in interval notation.

−1 < x ≤ 8−1 < x ≤ 8

From interval to inequality

Write the interval as an inequality.

(−∞, 1)(−∞, 1)

Solve a linear inequality, step by step

Solve the inequality. Give the answer as an inequality and in interval notation.

2x − 5 > 6x − 252x − 5 > 6x − 25

Solve a double inequality

Solve the double inequality. Give the answer as an inequality and in interval notation.

6 ≤ −4x + 2 < 266 ≤ −4x + 2 < 26

Largest value on a bounded region

What is the largest value of z = x + y when

• x ≥ 0
• y ≥ 0
• 5x + y ≤ 25
• 5x + 4y ≤ 40

Smallest value on an open region

What is the smallest value of z = 5x + 2y when

• x ≥ 0
• y ≥ 0
• 2x + y ≥ 7
• x + y ≥ 4