### ((x-6)/6-(x-2)/(x-6))/(36/(x-2)-4/9)

This encounters adding, subtracting and also finding the least usual multiple.

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## Step by action Solution ## Step 1 :

4 simplify — 9Equation in ~ the end of step 1 : (x-6) (x-2) 36 4 (—————-—————) ÷ (—————-—) 6 (x-6) (x-2) 9

## Step 2 :

36 leveling ————— x - 2Equation at the finish of action 2 : (x-6) (x-2) 36 4 (—————-—————) ÷ (———-—) 6 (x-6) x-2 9

## Step 3 :

Calculating the Least common Multiple :3.1 discover the Least common Multiple The left denominator is : x-2 The appropriate denominator is : 9

Number the times every prime factorappears in the administrate of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
3022
Product that allPrime Factors199

Number of times every Algebraic Factorappears in the administer of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
x-2101

Least usual Multiple: 9•(x-2)

Calculating multipliers :

3.2 calculation multipliers because that the 2 fractions represent the Least typical Multiple by L.C.M represent the Left Multiplier by Left_M represent the best Multiplier by Right_M represent the Left Deniminator by L_Deno signify the right Multiplier by R_DenoLeft_M=L.C.M/L_Deno=9Right_M=L.C.M/R_Deno=x-2

Making tantamount Fractions :

3.3 Rewrite the 2 fractions into tantamount fractionsTwo fountain are dubbed equivalent if they have the exact same numeric value. For instance : 1/2 and also 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are tantamount as well. To calculate equivalent fraction , main point the numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 36 • 9 —————————————————— = ————————— L.C.M 9 • (x-2) R. Mult. • R. Num. 4 • (x-2) —————————————————— = ————————— L.C.M 9 • (x-2)Adding fractions that have actually a common denominator :3.4 including up the two identical fractions include the two tantamount fractions i m sorry now have a typical denominatorCombine the molecule together, put the amount or distinction over the typical denominator then reduce to lowest state if possible:

36 • 9 - (4 • (x-2)) 332 - 4x ———————————————————— = ——————————— 9 • (x-2) 9 • (x - 2)Equation in ~ the finish of action 3 : (x-6) (x-2) (332-4x) (—————-—————) ÷ ———————— 6 (x-6) 9•(x-2)

## Step 4 :

x - 2 simplify ————— x - 6Equation at the finish of step 4 : (x - 6) (x - 2) (332 - 4x) (——————— - ———————) ÷ ——————————— 6 x - 6 9 • (x - 2)

## Step 5 :

x - 6 simplify ————— 6 Equation in ~ the finish of step 5 : (x - 6) (x - 2) (332 - 4x) (——————— - ———————) ÷ ——————————— 6 x - 6 9 • (x - 2)

## Step 6 :

Calculating the Least common Multiple :6.1 uncover the Least usual Multiple The left denominator is : 6 The best denominator is : x-6

Number of times every prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2101
3101
Product of allPrime Factors616

Number the times each Algebraic Factorappears in the administrate of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
x-6011

Least typical Multiple: 6•(x-6)

Calculating multipliers :

6.2 calculation multipliers for the 2 fractions signify the Least typical Multiple by L.C.M denote the Left Multiplier through Left_M represent the ideal Multiplier by Right_M denote the Left Deniminator by L_Deno denote the appropriate Multiplier by R_DenoLeft_M=L.C.M/L_Deno=x-6Right_M=L.C.M/R_Deno=6

Making identical Fractions :

6.3 Rewrite the two fractions into indistinguishable fractions

L. Mult. • L. Num. (x-6) • (x-6) —————————————————— = ————————————— L.C.M 6 • (x-6) R. Mult. • R.

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Num. (x-2) • 6 —————————————————— = ————————— L.C.M 6 • (x-6)Adding fractions that have a common denominator :6.4 including up the two indistinguishable fractions

(x-6) • (x-6) - ((x-2) • 6) x2 - 18x + 48 ——————————————————————————— = ————————————— 6 • (x-6) 6 • (x - 6) Equation at the end of action 6 : (x2 - 18x + 48) (332 - 4x) ——————————————— ÷ ——————————— 6 • (x - 6) 9 • (x - 2)

## Step 7 :

x2-18x+48 332-4x divide ————————— by ——————— 6•(x-6) 9•(x-2)7.1 separating fractions To division fractions, write the divison as multiplication by the reciprocal of the divisor :

x2 - 18x + 48 332 - 4x x2 - 18x + 48 9 • (x - 2)————————————— ÷ ——————————— = ————————————— • ——————————— 6 • (x - 6) 9 • (x - 2) 6 • (x - 6) (332 - 4x)

## Step 8 :

Pulling out prefer terms :8.1 pull out like factors:332 - 4x=-4•(x - 83)

Trying to variable by separating the center term8.2Factoring x2 - 18x + 48 The an initial term is, x2 that coefficient is 1.The middle term is, -18x that coefficient is -18.The critical term, "the constant", is +48Step-1 : main point the coefficient of the an initial term by the continuous 1•48=48Step-2 : discover two factors of 48 who sum equals the coefficient that the middle term, i m sorry is -18.

 -48 + -1 = -49 -24 + -2 = -26 -16 + -3 = -19 -12 + -4 = -16 -8 + -6 = -14 -6 + -8 = -14

For tidiness, print of 14 lines which failed to discover two together factors, to be suppressedObservation : No 2 such factors can be found !! Conclusion : Trinomial have the right to not it is in factored

## Final result :

3 • (x2 - 18x + 48) • (x - 2) ————————————————————————————— -8 • (x - 6) • (x - 83)