Factoring/Simplify
Factor:
4x^2+4x
4x(x+1)
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
The sum of two numbers is 12. The sum of their reciprocals is 3/8. What are the numbers?
The numbers are 4 and 8
Factor:
x^2-25
(x+5)(x-5)
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
Two consecutive numbers are represented by x and x+1. If six is added to the first number and two is subtracted from the second number, the quotient of the new numbers 9/2. Determine the numbers.
3,4
Factor:
4x-8
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)
Solve the rational equation (and check for extraneous solutions):
2+(x^2-4)/(x+3)=(-3x-2)/(x+3)
x = -4, x = -1
A laser printer paints 24 more sheets per minute then an ink-jet printer. If it takes the two printers a total of 14 min to print 490 pages, what is the printing rate of the ink-jet printer?
5.5 pages per minute.
Simplify:
(6x+30)/(x^2+8x+15)
6/(x+3)
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
A French club collected the same amount from each student going on a trip to Winnipeg. When six students could not go, each student was charged an extra three dollars. If the total cost was $540, how many students went on the trip?
Simplify:
(2x^2-10x)/(4x^2-20x)
1/2
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
A speed boat can travel 108km downstream in the same time it can travel 78km upstream. If the current in the river is 10km/hr, what is the speed of the boat in still water?
62km/hr in still water.