Math, asked by harshjanghu79, 11 months ago

x^-3 -y^-3/x^-3 y^-1 +(xy)^2 +y^-3 x^-1​

Answers

Answered by harsh6724
0

(x1/3-y1/3)(x2/3-x1/3y1/3+y2/3)

Final result :

(x - y) • (3x2 - xy + 3y2)

——————————————————————————

27

Step by step solution :

Step 1 :

y2

Simplify ——

3

Equation at the end of step 1 :

(x1) (y1) (x2) (x1) (y1) y2

(————-————)•((————-(————•————))+——)

3 3 3 3 3 3

Step 2 :

y

Simplify —

3

Equation at the end of step 2 :

(x1) (y1) (x2) (x1) y y2

(————-————)•((————-(————•—))+——)

3 3 3 3 3 3

Step 3 :

x

Simplify —

3

Equation at the end of step 3 :

(x1) (y1) (x2) x y y2

(————-————)•((————-(—•—))+——)

3 3 3 3 3 3

Step 4 :

x2

Simplify ——

3

Equation at the end of step 4 :

(x1) (y1) x2 xy y2

(————-————)•((——-——)+——)

3 3 3 9 3

Step 5 :

Calculating the Least Common Multiple :

5.1 Find the Least Common Multiple

The left denominator is : 3

The right denominator is : 9

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

3 1 2 2

Product of all

Prime Factors 3 9 9

Least Common Multiple:

9

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 = 3

Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. x2 • 3

—————————————————— = ——————

L.C.M 9

R. Mult. • R. Num. xy

—————————————————— = ——

L.C.M 9

Adding fractions that have a common denominator :

5.4 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:

x2 • 3 - (xy) 3x2 - xy

————————————— = ————————

9 9

Equation at the end of step 5 :

(x1) (y1) (3x2-xy) y2

(————-————)•(————————+——)

3 3 9 3

Step 6 :

Step 7 :

Pulling out like terms :

7.1 Pull out like factors :

3x2 - xy = x • (3x - y)

Calculating the Least Common Multiple :

7.2 Find the Least Common Multiple

The left denominator is : 9

The right denominator is : 3

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

3 2 1 2

Product of all

Prime Factors 9 3 9

Least Common Multiple:

9

Calculating Multipliers :

7.3 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 = 1

Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

7.4 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. x • (3x-y)

—————————————————— = ——————————

L.C.M 9

R. Mult. • R. Num. y2 • 3

—————————————————— = ——————

L.C.M 9

Adding fractions that have a common denominator :

7.5 Adding up the two equivalent fractions

x • (3x-y) + y2 • 3 3x2 - xy + 3y2

——————————————————— = ——————————————

9 9

Equation at the end of step 7 :

(x1) (y1) (3x2-xy+3y2)

(————-————)•————————————

3 3 9

Step 8 :

y

Simplify —

3

Equation at the end of step 8 :

(x1) y (3x2 - xy + 3y2)

(———— - —) • ————————————————

3 3 9

Step 9 :

x

Simplify —

3

Equation at the end of step 9 :

x y (3x2 - xy + 3y2)

(— - —) • ————————————————

3 3 9

Step 10 :

Adding fractions which have a common denominator :

10.1 Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x - (y) x - y

——————— = —————

3 3

Equation at the end of step 10 :

(x - y) (3x2 - xy + 3y2)

——————— • ————————————————

3 9

Step 11 :

Trying to factor a multi variable polynomial :

11.1 Factoring 3x2 - xy + 3y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

(x - y) • (3x2 - xy + 3y2)

——————————————————————————

27

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