s=ut+12at2

Rewrite the equation as ut+12at2=s.

ut+12at2=s

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

1,2at2,1

Since 1,2at2,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,2,1 then find LCM for the variable part a1,t2.

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The number 1 is not a prime number because it only has one positive factor, which is itself.

Not prime

Since 2 has no factors besides 1 and 2.

2 is a prime number

The number 1 is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of 1,2,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2

The factor for a1 is a itself.

a1=a

a occurs 1 time.

The factors for t2 are t⋅t, which is t multiplied by each other 2 times.

t2=t⋅t

t occurs 2 times.

The LCM of a1,t2 is the result of multiplying all prime factors the greatest number of times they occur in either term.

a⋅t⋅t

Multiply t by t by adding the exponents.

Move t.

a⋅(t⋅t)

Multiply t by t.

a⋅t2

at2

The LCM for 1,2at2,1 is the numeric part 2 multiplied by the variable part.

2at2

2at2

Multiply each term in ut+12at2=s by 2at2 in order to remove all the denominators from the equation.

ut⋅(2at2)+12at2⋅(2at2)=s⋅(2at2)

Simplify each term.

Rewrite using the commutative property of multiplication.

2(ut)(at2)+12at2⋅(2at2)=s⋅(2at2)

Multiply t by t2 by adding the exponents.

Move t2.

2(u(t2t))a+12at2⋅(2at2)=s⋅(2at2)

Multiply t2 by t.

Raise t to the power of 1.

2(u(t2t1))a+12at2⋅(2at2)=s⋅(2at2)

Use the power rule aman=am+n to combine exponents.

2(ut2+1)a+12at2⋅(2at2)=s⋅(2at2)

2(ut2+1)a+12at2⋅(2at2)=s⋅(2at2)

Add 2 and 1.

2(ut3)a+12at2⋅(2at2)=s⋅(2at2)

2(ut3)a+12at2⋅(2at2)=s⋅(2at2)

Rewrite using the commutative property of multiplication.

2ut3a+212at2(at2)=s⋅(2at2)

Cancel the common factor of 2.

Factor 2 out of 2at2.

2ut3a+212(at2)(at2)=s⋅(2at2)

Cancel the common factor.

2ut3a+212(at2)(at2)=s⋅(2at2)

Rewrite the expression.

2ut3a+1at2(at2)=s⋅(2at2)

2ut3a+1at2(at2)=s⋅(2at2)

Cancel the common factor of at2.

Cancel the common factor.

2ut3a+1at2(at2)=s⋅(2at2)

Rewrite the expression.

2ut3a+1=s⋅(2at2)

2ut3a+1=s⋅(2at2)

2ut3a+1=s⋅(2at2)

Rewrite using the commutative property of multiplication.

2ut3a+1=2sat2

2ut3a+1=2sat2

Solve for t s=ut+1/(2at^2)