add or subtract rational expressions
4x/10 - 7/10
4x-7/10
X^2+7x-18=0
(X+9)(x-2)=0
1/3p + 4/5p
17/15p
X2+8x-5=0
X=-4+sqrt(21)
A number tripled and then increased by 5 is 29. What is the number?
Let the number be X. 3X + 5 = 29. 3X = 24. X = 8.
3/5x+15 + 6/(x+3)-5
9/5(x+3)
x^2-5x-14=0
(X-7)(x+2)=0
9/10q - 2/5q
1/2q
X2+6x-11=0
X=-3+2sqrt(5)
The sum of two consecutive numbers is 41. What are the numbers?
Let the numbers be X and X + 1. X + (X + 1) = 41. 2X + 1 = 41. 2X = 40. X = 20. The numbers are 20 and 21.
5/y+4 - 3y/(y+4)(y-2)
2(y-5)/(y+4)(y-2)
X^3+4x^2-9x-36
(X-3)(x+3)(x+4)
3/7r + 5/6r
53/42r
X2+10x+4=0
X=-5+sqrt(21)
Brian charges $20 plus $4 for every window (n) he cleans. If a house has 7 windows, how much will he charge?
Charge = $20 + $4n. For n=7, Charge = $20 + $4 * 7 = $20 + $28 = $48.
7/6x + 5/6x
12/6x Or 2/x
X^2-2x-24
(X-6)(x+4)
7/8s - 1/3s
13/24s
X2-4x-3=0
X=2+sqrt(7)
The length of a rectangle is 10 feet more than twice its width. If the perimeter is 170 feet, what is the width?
Let width = W, Length = 2W + 10. Perimeter = 2 * (Length + Width). 170 = 2 * ( (2W + 10) + W ). 170 = 2 * (3W + 10). 85 = 3W + 10. 75 = 3W. W = 25 feet.
9/x+6 - 2/x-4
7x-48/(x+6)(x-4)
3x^2 -5x-12
(3x+4)(x-3)
5/12t + 3/4t
7/6t
X2-2x-1=0
X=1+sqrt(2)
Simplify: 4(X + 3) + 2X
Distribute the 4: 4X + 12 + 2X. Combine like terms: (4X + 2X) + 12 = 6X + 12.