Special Products & Factoring
Multiply:
(x-2)(x+7)
x^2+5x-14
Divide
(6x^3+2x^2+11x-10)/(3x-2)
2x^2+2x+5
Simplify:
x/(x+y)+y/(x-y)
(x^2+y^2)/(x^2-y^2)
Find all discontinuities of the rational function below and tell which feature each discontinuity represents.
f(x)=5/(x^2-2x-8)
VA @ x = -2
VA @ x = 4
State the domain and solve the equation, noting any extraneous solutions.
x+(2x)/(x-1)=(3-x)/(x-1)
S = {-3}, 1 is extr. sol.
x!=1
Multiply:
(12c-7d)(12c+7d)
144c^2-49d^2
Simplify:
(x^2-4)/(2x-4) cdot 2/(x+2)
1
Simplify:
(x+3)/(x-3)-(x-3)/(x+3)
(12x)/(x^2-9)
Find all discontinuities of the rational function below and tell which feature each discontinuity represents.
f(x)=(x-3)/(x^2-2x-3)
VA @ x = -1
RD @
(3,1/4)
State the domain and solve the equation, noting any extraneous solutions.
(4x)/(x-1)-(5x)/(x-2)=2/(x^2-3x+2)
S = {-1, -2}
x!=1,2
Multiply:
(2m-k)^2
4m^2-4mk+k^2
Simplify:
(x^2-9)/(x^2+x)-:(3-x)/(x^2-1)
-(x^2+2x-3)/x
Simplify:
(2y)/(x-2y)^2+1/(x-2y)
x/(x-2y)^2
Find all discontinuities of the rational function below and tell which feature each discontinuity represents.
f(x)=(3x+3)/(x^3+1)
RD @ (-1, 1)
State the domain and solve the equation, noting any extraneous solutions.
x/(x^2-2x+1)=2/(x+1)+4/(x^2-1)
S = {2}, -1 is extr. sol.
x!=1, -1
Factor Completely:
x^8-y^8
(x^4+y^4)(x^2+y^2)(x+y)(x-y)
Simplify using long division:
(6x^3+2x^2+11x-10)/(3x-2)
2x^2+2x+5
Simplify:
(4x)/(x+y)^2-4/(x+y)
-(4y)/(x+y)^2
Find all discontinuities of the rational function below and tell which feature each discontinuity represents.
f(x)=(x^2-x-6)/(x^2+3x+2)
RD @ (-2, 5)
VA @ x = -1
State the domain and solve the equation, noting any extraneous solutions.
x/(x+2)+7/(x-5)=14/(x^2-3x-10)
S = {0}, -2 is extr. sol.
x!=-2, 5
Factor completely:
81x^2+108x+36
9(3x+2)^2
Simplify using long division:
(x^3+5x^2-20)/(x+3)
x^2+2x-6-2/(x+3)
Simplify:
5/(3(a-b))+3/(2(b-a))
1/(6(a-b))
Find all discontinuities of the rational function below and tell which feature each discontinuity represents.
f(x)=[(x+2)(x+3)]/[(x+1)(x-2)(x+3)]
VA @ x = -1
VA @ x = 2
RD @
(-3,-1/10)
State the domain and solve the equation, noting any extraneous solutions.
2/(x+2)-x/(2-x)=(x^2+4)/(x^2-4)
O/
, 2 is extr. sol.
x!=-2,2
Factor completely:
5j^5+5000j^2
5j^2(j+10)(j^2-10j+100)
Simplify:
(12+6/x)/(12-9/x^2)
(2x)/(2x-1)
Simplify:
2x+5-(x^2+2x-15)/(x-3)
x
Find all discontinuities of the rational function below and tell which feature each discontinuity represents.
f(x)=(x+1)/(x^3+3x^2-6x-8)
VA @ x = -4
VA @ x = 2
RD @
(-1,-1/9)
State the domain and solve the equation, noting any extraneous solutions.
x/(x+4)+4/(x-4)=(x^2+16)/(x^2-16)
{all real nos.,
x!=4,-4}
x!=4,-4