Simplifying Rational Expressions
Simplify the rational expression.
(x^2+5x-14)/(x^2-4x+4)
(x+7)/(x-2)
Solve the equation.
5/x=7/(x+2)
x=5
Multiply and simplify.
(80x^4)/(y^3) *(xy)/(5x^2)
(16x^3)/y^2
Subtract the expressions and simplify.
3/(4x) - 1/(4x)
(2)/(4x)
The values of x that make f(x)=0. Also called x-intercepts when talking about the graph of the function.
Zeros of a Function
Simplify the rational expression.
(x^2-9x+14)/(x^2-5x-14)
(x-2)/(x+2)
Solve the equation.
(x-4)/(x-1)=10/(x+7)
x=-2, 9
Multiply and simplify:
(6x^2-18x)/(x^2-10x+21) * (x^2-14x+49)/(3x^2)
(2(x-7))/x
Add the expressions and simplify.
(12x^2)/(6x)+(7x-2)/(6x)
(12x^2+7x-2)/(6x)
A fraction made of two polynomials
Rational Expression
Simplify the rational expression.
(x^2-36)/(x^2+12x+36)
(x-6)/(x+6)
Solve the equation.
(x+12)/3=(2x+3)/(x+2)
x= -5, -3
Divide and simplify.
(5x^2y^3)/(x^7) div (30xy^4)/(y^3)
y^2/(6x^6)
Find the Least Common Multiple (LCM):
10x^2-15x
5x^3
5x^2(2x-3)
An equation that contains a rational expression
Rational Equation
Simplify the rational expression.
(2x^2+2x-4)/(x^2-5x-14)
(2(x-1))/(x-7)
Solve the equation.
1/(x+6)+(x+1)/x=13/(x+6)
x=2,3
Multiply and simplify.
(x-3)/(2x-8) * (6x^2-96)/(x^2-9)
(3(x+4))/(x+3)
Add the expressions and simplify.
x/(x^2+3x-10) + 5/(x^2+3x-10)
(1)/(x-2)
A line that a graph approaches(doesn't cross)
Asymptote
Simplify the rational expression.
(8x^2+10x-3)/(6x^2+13x+6)
(4x-1)/(3x+2)
Solve the equation.
(3x)/(x+1)+6/(2x)=7/x
x=-2/3, 2
Divide and simplify.
(3x+27)/(6x-48) div (x^2+9x)/(x^2-4x-32)
(x+4)/(2x)
Subtract the expressions and simplify.
(2x)/(x^2+5x-14) - (x+3)/(x^2+5x-14)
(x-3)/(x^2+5x-14)
A solution of an equation derived from the original equation but is not a solution to the original equation
Extraneous Solution