Applications of Rational Functions CR A1

x²+7x+6/x²+7x 
÷
x²+x/x²-49

• 1 / x²
• x + 6
• x² - x - 42 / x²
• x + 6 / x + 7

3x-3x²/x² + 4x-5
×
x²+x-20/3x

• - x + 4
• 3x - 5
• x + 7
• 3x² + 1

An isosceles triangle has two sides of length 4x + 6. The perimeter of the triangle is 14x + 21. Determine the ratio of the base to the perimeter.

• 3 / 7
• 7 / 3
• 3 / 7x
• 7 / 3x

2/x²
+
x+1/x²+x

• x + 1 / x²
• 2x + 2 / x²
• x - 2 / x²
• x + 2 / x²

1 / x
-
x / 2x²+4x

• x+2 / 2x²(x+2)
• 2 / 2x(x+2)
• x+4 / 2x²+4x
• 3x+2 / 2x(x+2)

3 / x+1
=
9 / 4x+5
Solve for x

• x = 1
• x = 4
•  x = -3
• x = -2

6 / x-3
=
8x² / x²-9
-
4x / x+3

• x = -3
• x = 3/2
• x = -3 or x = 3/2
• No real solution

x+2 / 2x-2
-
-2x-1 / x²-4x+3

• x+4 / 2(x-3)
• x+3 / 4(x-1)
• x²+7 / 2x-1
• x+1 / 3(x-3)

2x / x+1 -
x+1 / x =
2 / x² +x

• x =3
• x = -1
• x = -1 or x = 3
• No real solutions

2 / x-2  +
6x / x²-4 =
3 / x+2 

• x = -2
• x = 2
• x = -2 or x = 2
• No real solutions