### p1v1/t1=p2v2/t2

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

You are watching: P1v1/t1=p2v2/t2 solve for t2

## Step by Step Solution

### Reformatting the input :

Changes made to your input should not affect the solution: (1): “t2” was replaced by “t^2”. 5 more similar replacement(s).

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : p^1*v^1/t^1-(p^2*v^2/t^2)=0

## Step by step solution :

## Step 1 :

v2 Simplify —— t2Equation at the end of step 1 : (v1) v2 ((p1)•————)-((p2)•——) = 0 (t1) t2

## Step 2 :

v Simplify — tEquation at the end of step 2 : v p2v2 ((p1) • —) – ———— = 0 t t2

## Step 3 :

Calculating the Least Common Multiple :3.1 Find the Least Common Multiple The left denominator is : t The right denominator is : t2

Number of times each Algebraic Factorappears in the factorization of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = Max{Left,Right}t | 1 | 2 | 2 |

Least Common Multiple: t2

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=tRight_M=L.C.M/R_Deno=1

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 : 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.

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L. Mult. • L. Num. pv • t —————————————————— = —————— L.C.M t2 R. Mult. • R. Num. p2v2 —————————————————— = ———— L.C.M t2 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:

pv • t – (p2v2) pvt – p2v2 ——————————————— = —————————— t2 t2

## Step 4 :

Pulling out like terms :4.1 Pull out like factors:pvt – p2v2=-pv•(pv – t)

Equation at the end of step 4 : -pv • (pv – t) —————————————— = 0 t2

## 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:

-pv•(pv-t) —————————— • t2 = 0 • t2 t2 Now, on the left hand side, the t2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:-pv • (pv-t)=0

Theory – Roots of a product :5.2 A product 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 solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

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Solving a Single Variable Equation:5.3Solve-pv=0 Setting any of the variables to zero solves the equation:p=0v=0

Solving a Single Variable Equation:

5.4Solvepv-t=0 In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.We shall not handle this type of equations at this time.

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