x^2+x+1/(x+2)^3 = 1/x+2 -3/ (x+2)^2 + k/(x+2)^3 then k
a)1
b)2
c)3
d)5
Answers
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2+x+1/(x+2)^3-(1/x+2-3/(x+2)^2+k/(x+2)^3)=0
STEP
1
:
k
Simplify ————————
(x + 2)3
Equation at the end of step
1
:
1 1 3 k
(((x2)+x)+————————)-(((—+2)-————————)+——————) = 0
((x+2)3) x ((x+2)2) (x+2)3
STEP
2
:
3
Simplify ————————
(x + 2)2
Equation at the end of step
2
:
1 1 3 k
(((x2)+x)+————————)-(((—+2)-——————)+——————) = 0
((x+2)3) x (x+2)2 (x+2)3
STEP
3
:
1
Simplify —
x
Equation at the end of step
3
:
1 1 3 k
(((x2)+x)+————————)-(((—+2)-——————)+——————) = 0
((x+2)3) x (x+2)2 (x+2)3
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x as the denominator :
2 2 • x
2 = — = —————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 + 2 • x 2x + 1
————————— = ——————
x x
Equation at the end of step
4
:
1 (2x+1) 3 k
(((x2)+x)+————————)-((——————-——————)+——————) = 0
((x+2)3) x (x+2)2 (x+2)3
STEP
5
:
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : x
The right denominator is : (x+2)2
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 1 0 1
x+2 0 2 2
Least Common Multiple:
x • (x+2)2
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = (x+2)2
Right_M = L.C.M / R_Deno = x