### 8/3=2x/3x-15

This deals with adding, subtracting and finding the least common multiple.

## Step by Step Solution ### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 8/3-(2*x/3*x-15)=0

## Step 1 :

x Simplify — 3Equation at the end of step 1 : 8 x — - (((2 • —) • x) - 15) = 0 3 3

## Step 2 :

Rewriting the whole as an Equivalent Fraction :2.1Subtracting a whole from a fraction Rewrite the whole as a fraction using 3 as the denominator :

15 15 • 3 15 = —— = —————— 1 3 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 :2.2 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:

2x2 - (15 • 3) 2x2 - 45 —————————————— = ———————— 3 3 Equation at the end of step 2 : 8 (2x2 - 45) — - —————————— = 0 3 3

## Step 3 :

8 Simplify — 3Equation at the end of step 3 : 8 (2x2 - 45) — - —————————— = 0 3 3

## Step 4 :

Trying to factor as a Difference of Squares:4.1 Factoring: 2x2-45 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. Note : -AB+ AB equals zero and is therefore eliminated from the expression.Check: 2 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares

Adding fractions which have a common denominator :

4.2 Adding fractions which have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

8 - ((2x2-45)) 53 - 2x2 —————————————— = ———————— 3 3 Trying to factor as a Difference of Squares:4.3 Factoring: 53 - 2x2 Check: 53 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares

Equation at the end of step 4 :

53 - 2x2 ———————— = 0 3

## Step 5 :

When a fraction equals zero :5.1 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:

53-2x2 —————— • 3 = 0 • 3 3 Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:53-2x2=0

Solving a Single Variable Equation:5.2Solve:-2x2+53 = 0Subtract 53 from both sides of the equation:-2x2 = -53 Multiply both sides of the equation by (-1) : 2x2 = 53 Divide both sides of the equation by 2:x2 = 53/2 = 26.500 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ 53/2 The equation has two real solutions These solutions are x = ±√ 26.500 = ± 5.14782