drdq=178-q-1.5q2

Cancel the common factor.

drdq=178-q-1.5q2

Rewrite the expression.

rq=178-q-1.5q2

rq=178-q-1.5q2

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

q,1,1,1

Since q,1,1,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,1,1,1 then find LCM for the variable part q1.

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

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

1

The factor for q1 is q itself.

q1=q

q occurs 1 time.

The LCM of q1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

q

q

Multiply each term in rq=178-q-1.5q2 by q in order to remove all the denominators from the equation.

rq⋅q=178⋅q-q⋅q-1.5q2⋅q

Cancel the common factor of q.

Cancel the common factor.

rq⋅q=178⋅q-q⋅q-1.5q2⋅q

Rewrite the expression.

r=178⋅q-q⋅q-1.5q2⋅q

r=178⋅q-q⋅q-1.5q2⋅q

Simplify each term.

Multiply q by q by adding the exponents.

Move q.

r=178q-(q⋅q)-1.5q2⋅q

Multiply q by q.

r=178q-q2-1.5q2⋅q

r=178q-q2-1.5q2⋅q

Multiply q2 by q by adding the exponents.

Move q.

r=178q-q2-1.5(q⋅q2)

Multiply q by q2.

Raise q to the power of 1.

r=178q-q2-1.5(q1q2)

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

r=178q-q2-1.5q1+2

r=178q-q2-1.5q1+2

Add 1 and 2.

r=178q-q2-1.5q3

r=178q-q2-1.5q3

r=178q-q2-1.5q3

r=178q-q2-1.5q3

Rewrite the equation as 178q-q2-1.5q3=r.

178q-q2-1.5q3=r

Solve for q (dr)/(dq)=178-q-1.5q^2