Rational Expressions Flashcards
r+5 / r**2+r-12. What is the domain?
Domain is what should not be x. It is always what makes the denominator 0.
We take whats under the fraction and set it equal to 0,
facor it to get (r-3)(r+4)=0, calculate both equatiobs out and get =/3 and -4
4/7 * 5/8
crossover gcf, make it to 1/7 and 5/2 first then multiply
a2/b3 * b2/a5
crossover to 1/b * 1/a**3
Division of fractions.
1/8 / 3/4
Swith position of 2nd fraction and then multiply. 1/8 * 4/3
Long division of polynominals
x**2-2x-24 / x-5
write as
x-5| x2-2x-24 # from the line it goes horizontal over 24
you take the first sign, so x, and look what has to be multiplied to get x2. What has to be multiplied you multiply with the second term, so -5. You subtract the second line from the first, then put the next term next to it.
you get the reminder 9. Put it over the division line with 9/x-5. What is over the line is your result: x+3+9/x-5
How to find the least common denominator? (the smallest value that is divisible by two or more specified denominators
a+2/8 and a-4/12
you cann see that it is 24, but you can also calculate it by using prime facorization for both:
8=222
12=322
putting them together. Ever value only one, so: 222 and then looking what isn´t in there what 12 has, so: 222*3
then put 24 under fraction and multiply every term upfront: 3a+6/24 and 2a-8/24
5x/x+1 - 3/x-1
find least common denominator, in this case:(x+1)(x-1). Look what the fractions where missing of that LCD and multiply it to the nominator.
5x**2-5x / (x+1)(x-1)
3x+3 / (x+1)(x-1)
then final step putting it together:
5x**2-5x - 3x+3
____________
(x+1)(x-1)
x/4=12/16 find x
you can use cross multiplication. x16 and 412 you get
48=16x now sole equation
Tim needs 2 hours to drive 90 miles, how long does it take him to drive 360?
8 hours. Cross multiplication is the key here
