Question

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​

Answer 1

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