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Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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Solving Equations Involving Rational Expressions

To solve an equation with rational expressions, we do not convert the rational expressions to ones with a common denominator. Instead, we multiply each side by the LCD to eliminate the denominators.

Example 1

An equation with two solutions

Solve

Solution

			= x(x + 20)10	Multiply each side by x(x + 20).
			= x(x + 20)10	Distributive property
(x + 20)200 + x(300)			= (x² + 20x)10	Simplify.
200x + 4000 + 300x			= 10x² + 200x
4000 + 300x			= 10x²	Combine like terms.
400 + 30x			= x²	Divide each side by 10.
0			= x² - 30x - 400
0			= (x - 40)(x + 10)	Factor.
x - 40 = 0	or	x + 10	= 0	Set each factor equal to 0.
x = 40	or	x	= -10

Check these values in the original equation. The solution set is {-10, 40}.