Simplify and expand the following expression:
\dfrac{NUMERATOR1}{DENOMINATOR1}SIGN
\dfrac{NUMERATOR2}{DENOMINATOR2}
In order to add expressions, they must have a common denominator.
In order to subtract expressions, they must have a common denominator.
Get both fractions over a common denominator of (DENOMINATOR1)(DENOMINATOR2).
Multiply the first term by \dfrac{DENOMINATOR2}{DENOMINATOR2}:
\qquad\begin{align*}
\dfrac{NUMERATOR1}{DENOMINATOR1} \times \dfrac{DENOMINATOR2}{DENOMINATOR2}
& = \dfrac{(NUMERATOR1)(DENOMINATOR2)}{(DENOMINATOR1)(DENOMINATOR2)} \\
& = \dfrac{PRODUCT1}{(DENOMINATOR1)(DENOMINATOR2)}\end{align*}
Multiply the second term by \dfrac{DENOMINATOR1}{DENOMINATOR1}:
\qquad\begin{align*}
\dfrac{NUMERATOR2}{DENOMINATOR2} \times \dfrac{DENOMINATOR1}{DENOMINATOR1}
& = \dfrac{(NUMERATOR2)(DENOMINATOR1)}{(DENOMINATOR2)(DENOMINATOR1)} \\
& = \dfrac{PRODUCT2}{(DENOMINATOR2)(DENOMINATOR1)}\end{align*}
Now we have:
\qquad =
\dfrac{PRODUCT1}{(DENOMINATOR1)(DENOMINATOR2)} SIGN
\dfrac{PRODUCT2}{(DENOMINATOR2)(DENOMINATOR1)}
Now both terms have a common denominator we can simply add the numerators:
\qquad
\dfrac{PRODUCT1 + PRODUCT2}{(DENOMINATOR1)(DENOMINATOR2)}
Now both terms have a common denominator we can subtract the numerators:
\qquad =
\dfrac{PRODUCT1 - (PRODUCT2)}{(DENOMINATOR1)(DENOMINATOR2)}
\qquad =
\dfrac{PRODUCT1 + PRODUCT2a}{(DENOMINATOR1)(DENOMINATOR2)}
\qquad = \dfrac{NUMERATOR}{(DENOMINATOR1)(DENOMINATOR2)}
Expand the denominator:
\qquad = \dfrac{NUMERATOR}{DENOMINATOR}
Simplify:
\qquad = \dfrac{NUMERSOL}{DENOMSOL}