1/x+1/y+1/z

This solution đơn hàng with adding, subtracting và finding the least common multiple.




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Step by Step Solution

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Step 1 :

1 Simplify — zEquation at the kết thúc of step 1 : 1 1 1 (— + —) + — x y z

Step 2 :

1 Simplify — yEquation at the kết thúc of step 2 : 1 1 1 (— + —) + — x y z

Step 3 :

1 Simplify — xEquation at the kết thúc of step 3 : 1 1 1 (— + —) + — x y z

Step 4 :

Calculating the Least Common Multiple :4.1 Find the Least Common Multiple The left denominator is : x The right denominator is : y

Number of times each Algebraic Factorappears in the factorization of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
x101
y011

Least Common Multiple: xy

Calculating Multipliers :

4.2 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_DenoLeft_M=L.C.M/L_Deno=yRight_M=L.C.M/R_Deno=x

Making Equivalent Fractions :

4.3 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value. For example : 1/2 & 2/4 are equivalent, y/(y+1)2 và (y2+y)/(y+1)3 are equivalent as well. Khổng lồ calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. Y —————————————————— = —— L.C.M xy R. Mult. • R. Num. X —————————————————— = —— L.C.M xyAdding fractions that have a common denominator :4.4 Adding up the two equivalent fractions địa chỉ cửa hàng the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce khổng lồ lowest terms if possible:

y + x x + y ————— = ————— xy xy Equation at the kết thúc of step 4 : (x + y) 1 ——————— + — xy z

Step 5 :

Calculating the Least Common Multiple :5.1 Find the Least Common Multiple The left denominator is : xy The right denominator is : z

Number of times each Algebraic Factorappears in the factorization of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
x101
y101
z011

Least Common Multiple: xyz

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_DenoLeft_M=L.C.M/L_Deno=zRight_M=L.C.M/R_Deno=xy

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (x+y) • z —————————————————— = ————————— L.C.M xyz R. Mult. • R.

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Num. Xy —————————————————— = ——— L.C.M xyzAdding fractions that have a common denominator :5.4 Adding up the two equivalent fractions

(x+y) • z + xy xy + xz + yz —————————————— = ———————————— xyz xyz

Final result :

xy + xz + yz ———————————— xyz