Simplify Rational Functions and state restrictions
(4d^2+8d)/(2d)
2(d+2)
d!=0
(x^2-16)/(x+3)*(x^2-9)/(x-4)
(x+4)(x-3);x!=-3,4
Find the VA(s), HA(s), hole(s) and intercepts of the graph:
f(x)=(x+3)/(x-2)
VA:x=2; HA:y=1; Hole:none
Intercepts: (0,-3/2) (-3,0)
"State the LCD and then perform the operation"
(3)/(12y)+(9)/(24)
"LCD"=24y;
(6+9y)/(24y)
(x+6)/(4x)+(3)/(2x)=(x+4)/(2x)
x=4
(6x^3+6x^2)/(2x^3-2x)
(3x)/(x-1);x!=-1,0,1
(7x^4)/(24y^5)-:(21x)/(12y^4)
(x^3)/(6y)
Describe the VA(s), HA(s), hole(s) and intercept(s) of the graph: f(x)=(x+3)/(x^2-9)
VA:x=3; HA:y=0;
Hole:(-3,-1/6)
Intercepts: (0,-1/3), no x-intercept
"State the LCD and then perform the operation"
1/x+(x-1)/5
"LCD"=5x
(x^2-x+5)/(5x)
(1)/(x^2-x)+(1)/(x)=(5)/(x^2-x)
x=5
((x+3)(x-3)(x^3+9x))/(x^2+9)
x(x+3)(x-3)
"defined for all real numbers"
(x^2)/(x+3) *(x^2+4x+3)/((x^2-2x)
(x(x+1)]/(x-2);x!=-3,0,2
Describe the VA(s), HA(s), hole(s) and intercept(s) of the graph:
y=(x^2+4x)/(x^2+3x-4)
VA:x=1; HA:y=1;
Hole:(-4, 4/5)
Intercepts: (0,0)
"State the LCD and then perform the operation"
(3)/(x+4)-(1)/(x+6)
"LCD"=(x+6)(x+4)
((2x+14))/((x+6)(x+4)
(1)/(x)+(3x+12)/(x^2-5x)=(7x-56)/(x^2-5x)
x=21
(x^2+13x+40)/(x^2-2x-35)
(x+8)/(x-7);x!=-5,7
(2x^2+5x-3)/(x^2-4x)*(2x^3-8x^2)/(x^2+6x+9)
(2x(2x-1))/(x+3);x!=-3,0,4
Describe the VA(s), HA(s), hole(s) and intercept(s) of the graph: f(x)=(3x^2-5x-2)/(x^2-3x+2)
VA:x=1; HA:y=3
Hole: (2,7)
Intercepts: (0,-1), (-1/3,0)
"State the LCD and then perform the operation"
x/(x^2-2x-8)-(4+x-x^2)/(x^2-2x-8)
"LCD"=(x-4)(x+2)
(x-2)/(x-4
(x+4)/(4)+(x-1)/(4)=(x+4)/(4x)
x=-2
x=1
(4x^2-12x+9)/(2x^2+15x-27)
(2x-3)/(x+9);x!=-9,3/2
(x^2-81)/(4x^2+27x-7)-:(x^2-5x-36)/(x^2+11x+28)
(x+9)/(4x-1)
Write the equation in standard form (not factored) for the graph that has VA @ x=2, HA @ y=1, Hole @ (-3, 2/5), y-intercept @ (0,-1/2) and x-intercept @ (-1,0)
f(x)=(x^2+4x+3)/(x^2+x-6)
"State the LCD and then perform the operation"
(x+1)/(4x^2-9)-(4)/(2x-3)
"LCD"=(2x-3)(2x+3)
(-7x-11)/{(2x-3)(2x+3)
1/(x-1)=(x)/(x+3)+3/5
x=2
x=-3/2