Factoring
Factor:
4x^2+4x
4x(x+1)
A positive integer is 4 less than another. The sum of the reciprocals of the two positive integers is 10/21 . Find the two integers.
3 and 7
To add or subtract rational expressions, you need a __________ __________.
common denominator
What strategy can you use to divide rational expressions?
“keep, change, flip”
(multiply by the reciprocal)
Excluded values of a rational expression will make the value of the denominator equal to _____.
0
Factor:
x^2-25
(x+5)(x-5)
A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/8. Find the two integers
4,8
Add the rational expressions and simplify your answer:
5/(14x) + 3/(2x)
13/(7x)
TRUE OR FALSE:
When multiplying or dividing a rational expression, you do NOT need a common denominator.
TRUE
Solve the rational equation (and check for extraneous solutions):
(x+3)/5 = (x+1)/2
x=1/3
Factor:
x^2+13x+42
(x+6)(x+7)
Determine the value of x if the perimeter of a rectangle is 50cm and the sides are 35/(5x-10) and 6x/(x-2)
x=3
Find the common denominator of the rational expressions:
(2p)/(p+6) and 2/(5p-4)
(5p-4)(p+6)
Multiply the rational expressions:
1/(n+5) * (9n+45)/(n+5)
9/(n+5)
(2+x)/14 + x/2=(3x-2)/7
x=-3
Factor:
2x^2-2
2(x+1)(x-1)
Mary spent the first 120 miles of her road trip in traffic. When the traffic cleared, she was able to drive twice as fast for the remaining 300 miles. If the total trip took 9 hours, then how fast was she moving in traffic?
Mary Averages 30 miles per hour
Subtract the rational expression:
4/(v+4) -3/4
(4-3v)/(4(v+4)
Divide the rational expressions:
(x-8)/(7x+14) div 1/(x+2)
(x-8)/7
Solve the rational equation (and check for extraneous solutions):
8/(x+3) = (x+1)/(x+6)
x=9,-5
Factor:
6x^2+10x-4
2(3x-1)(x+2)
A passenger train can travel, on average 20miles per hour faster than a freight train. If the passenger train covers 390 miles in the same time it takes the freight train to cover 270 miles, then how fast is each train?
65 miles- passenger train
45 mile- freight train
Add the rational expressions:
4/(3x+3)+1/(x-2)
(7x-5)/((3x+3)(x-2))
Multiply the rational expression:
(x+1)/(x^2-x-6) * (x^2+4x+4)/(x^2-4)
(x+1)/((x-3)(x-2))
Solve the rational equation (and check for extraneous solutions):
1/x+3/(x-4) = (2x+8)/(x^2-4x)
x=6