Simplify and expand the following expression:
\dfrac{N1}{D1}SIGN1
\dfrac{N2}{D2}SIGN2
\dfrac{N3}{D3}
First find a common denominator by finding the least common multiple of the denominators.
Try factoring the denominators.
We can factor a F1 out of denominator in the first term:
\qquad\dfrac{N1}{D1} = \dfrac{N1}{F1(TERM1)}
We can factor a F2 out of denominator in the second term:
\qquad\dfrac{N2}{D2} = \dfrac{N2}{F2(TERM2)}
We can factor the quadratic in the third term:
\qquad\dfrac{N3}{D3} = \dfrac{N3}{(TERM1)(TERM2)}
Now we have:
\qquad
\dfrac{N1}{D1.toStringFactored()}SIGN1
\dfrac{N2}{D2.toStringFactored()}SIGN2
\dfrac{N3}{(TERM1)(TERM2)}
The least common multiple of the denominators is:
\qquadCOMMON_DENOM
In order to get the first term over
COMMON_DENOM, multiply by
\dfrac{D2.toStringFactored()}{D2.toStringFactored()}:
\qquad
\dfrac{N1}{D1.toStringFactored()} \times
\dfrac{D2.toStringFactored()}{D2.toStringFactored()} =
\dfrac{PRODUCT1.toStringFactored()}{COMMON_DENOM}
In order to get the second term over
COMMON_DENOM, multiply by
\dfrac{D1.toStringFactored()}{D1.toStringFactored()}:
\qquad
\dfrac{N2}{D2.toStringFactored()} \times
\dfrac{D1.toStringFactored()}{D1.toStringFactored()} =
\dfrac{PRODUCT2.toStringFactored()}{COMMON_DENOM}
In order to get the third term over
COMMON_DENOM, multiply by
\dfrac{F1 * F2}{F1 * F2}:
\qquad
\dfrac{N3}{(TERM1)(TERM2)} \times
\dfrac{F1 * F2}{F1 * F2} =
\dfrac{PRODUCT3.toStringFactored()}{COMMON_DENOM}
Now we have:
\qquad
\dfrac{PRODUCT1.toStringFactored()}{COMMON_DENOM} SIGN1
\dfrac{PRODUCT2.toStringFactored()}{COMMON_DENOM} SIGN2
\dfrac{PRODUCT3.toStringFactored()}{COMMON_DENOM}
\qquad = \dfrac{
PRODUCT1.toStringFactored() + PRODUCT2a.toStringFactored() + PRODUCT3a.toStringFactored()}
{COMMON_DENOM}
Expand:
\qquad = \dfrac{PRODUCT1 + PRODUCT2a + PRODUCT3a}{DENOMINATOR}
\qquad = \dfrac{NUMERATOR}{DENOMINATOR}
Simplify:
\qquad = \dfrac{FINAL_N}{FINAL_D}