# Algebra Topics: Exponents

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

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## Step by Step Solution ### Rearrange:

Rearrange the equation by subtracting what is to lớn the right of the equal sign from both sides of the equation : 8/x-(1/8*x)=0

## Step 1 :

1 Simplify — 8Equation at the kết thúc of step 1 : 8 1 — - (— • x) = 0 x 8

## Step 2 :

8 Simplify — xEquation at the end of step 2 : 8 x — - — = 0 x 8

## Step 3 :

Calculating the Least Common Multiple :3.1 Find the Least Common Multiple The left denominator is : x The right denominator is : 8

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2033
Product of allPrime Factors188

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

Least Common Multiple: 8x

Calculating Multipliers :

3.2 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=8Right_M=L.C.M/R_Deno=x

Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value. For example : một nửa và 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.

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8 • 8 —————————————————— = ————— L.C.M 8x R. Mult. • R. Num. X • x —————————————————— = ————— L.C.M 8x Adding fractions that have a common denominator :3.4 Adding up the two equivalent fractions add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

8 • 8 - (x • x) 64 - x2 ——————————————— = ——————— 8x 8x Trying lớn factor as a Difference of Squares:3.5 Factoring: 64 - x2 Theory : A difference of two perfect squares, A2-B2can be factored into (A+B)•(A-B)Proof:(A+B)•(A-B)= A2 - AB+BA-B2= A2 -AB+ AB - B2 = A2 - B2Note : AB = ba is the commutative property of multiplication. Lưu ý : -AB+ AB equals zero và is therefore eliminated from the expression.Check: 64 is the square of 8Check: x2 is the square of x1Factorization is :(8 + x)•(8 - x)

Equation at the kết thúc of step 3 :

(x + 8) • (8 - x) ————————————————— = 0 8x

## Step 4 :

When a fraction equals zero :4.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here"s how:

(x+8)•(8-x) ——————————— • 8x = 0 • 8x 8x Now, on the left hand side, the 8x cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:(x+8) • (8-x)=0

Theory - Roots of a product :4.2 A hàng hóa of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to lớn solve as many equations as there are terms in the productAny solution of term = 0 solves sản phẩm = 0 as well.

Solving a Single Variable Equation:4.3Solve:x+8 = 0Subtract 8 from both sides of the equation:x = -8

Solving a Single Variable Equation:4.4Solve:-x+8 = 0Subtract 8 from both sides of the equation:-x = -8 Multiply both sides of the equation by (-1) : x = 8