For week 15 of precalculus 11 we started off monday doing 7.4 on adding and subtracting with binomial and trinomial denominators, 7.5 on wednesday, and 7.6 on thursday.
One thing I learned in lesson 7.4 that translated over to all the rest of the units, was how to multiply each fraction together by a common denominator.
If there was an expression like :
1/(x+1) – 2/(x+4) = 1
to combine the fraction to an entire common denominator, you have to multiply each of the numerators by the value(s) they don’t have in their denominator already
I.E. you would multiply the numerator 1 on the left side by (x+4) because that is the denominator it is missing, 2 by (x+1), and 1 on the right side by both (x+4) and (x+1)
New equation =
1(x+4) – 2(x+1) = (x+4)(x+1)
x + 4 – 2x – 2 = x2 + 5x + 1
= x2 + 6x – 1