Rational Expressions and Equations

Reducing

Simplify the expression

\frac{9 x^{2} - 16}{3 x - 4}

More examples

Cancelling the Common Factors

Simplify the rational expression:

\frac{9 x^{2} - 16}{3 x + 4}

More examples

Rewriting in Standard Form

Rewrite the rational expression

\frac{2 x^{2} - 5 x - 3}{x^{2} - 4}

in standard form.

More examples

Operations on Rational Expressions

\frac{x + \frac{1}{2}}{2 + \frac{1}{x}} =

More examples

Determining if the Point is a Solution

Is the point (3, -2) a solution to the equation

y = \frac{2 x - 5}{x + 1}

More examples

Finding the Domain

RATIONAL EXPRESSIONS Restriction on a variable in a denominator: Quadratic Find all excluded values for the expression. That is, find all values of

x

for which the expression is undefined.

\frac{x^{2} - 6 x + 8}{x^{2} - 1}

If there is more than one value, separate them with commas.

x =

More examples

Solving over the Interval

Solve the equation

\frac{3}{x - 2} - \frac{2}{x + 3} = 1

over the interval

[- 5, 4]

More examples

Finding the Domain and Range

Find the domain and range of the function

f (x) = \frac{1}{x + 3}

More examples

Solving Rational Equations

\frac{x}{(x + 2) (x - 2)} + \frac{4}{x - 2} = \frac{3}{x + 2}

More examples

Adding Rational Expressions

\frac{5}{a^{2} + 12 a + 36} + \frac{8}{a^{2} - 36}

More examples

Subtracting Rational Expressions

\frac{6 n}{n^{2} - 9} - \frac{3}{n + 3}

More examples

Multiplying Rational Expressions

Multiply the following rational expr

\frac{x^{2} + 2 x - 15}{x^{2} + (- 4) x - 12} \cdot \frac{x^{2} + 8 x + 12}{x^{2} - 9}

More examples

Finding the Equation Given the Roots

Use the rational zeros theorem to list all possible zeros of the function

f (x) = 7 x^{3} - 3 x^{2} - x + 2

Enter the possible zeros separated by commas. You do not need to factor the polynomial.

More examples

Finding the Asymptotes

f (x) = \frac{x - 1}{x^{2} - 1}

More examples

Finding the Constant of Variation

y = k x^{2}

, where

k

is a constant, and

y = 25

when

x = 5

, what is the value of

k

More examples

Finding the Equation of Variation

If y varies directly as the square of x and inversely as the cube root of z, where y = 9 when x = 3 and z = 8, find the equation of variation.

More examples

Reducing

Cancelling the Common Factors

Rewriting in Standard Form

Operations on Rational Expressions

Determining if the Point is a Solution

Finding the Domain

Solving over the Interval

Finding the Domain and Range

Solving Rational Equations

Adding Rational Expressions

Subtracting Rational Expressions

Multiplying Rational Expressions

Finding the Equation Given the Roots

Finding the Asymptotes

Finding the Constant of Variation

Finding the Equation of Variation

Popular Problems