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Simplifying rational expressions

Reduce to lowest terms, stating the restrictions on the variable.

2-r/r-2. < - - - I dont get how these become a -1. Restriction I know is 2.

4-4x^2/8x^3+8x^2-16x < - - Tried solving that one, but I keep getting the wrong answer.

*Consider rectangle shown with area of 24x^3-54x^2-15x with length side of 6x^2-15x. Write and simplify an expression for the length of the rectangle.

Part b to ^ that one. - - - > Determine the perimeter of the rectangle if x = 2V2 cm. Give answer in simplest radical form. (V is symbol for that radical, dont know how to make radical sign on computer)

Originally posted by: -Ayeshaa-

When two waves interfere, is there a loss of energy in the system?

True? Wouldn't nodes be present?

Originally posted by: akhl

There is no loss of energy. At nodes, the waves cancel each other but at antinodes, they get added. The total energy remains conserved.

Originally posted by: -Ayeshaa-

Simplifying rational expressions

Reduce to lowest terms, stating the restrictions on the variable.

2-r/r-2. < - - - I dont get how these become a -1. Restriction I know is 2.[/quote]

(2-r)/(r-2) = -(r-2)/(r-2) = -1

4-4x^2/8x^3+8x^2-16x = 4(1-x^2)/(8x)(x^2+x-2)
= (1-x^2)/(2x)(x^2+x-2)
= (1+x)(1-x)/(2x)(x+2)(x-1)
= -(1+x)(x-1)/(2x)(x+2)(x-1) => restriction: x is not equal to 0,-2,1
= -(1+x)/(2x)(x+2)
= -(x+1)/(2x^2+4x)

Addition and Subtraction of Rational Expressions.

Simplify:

x/4 + x+3/6 + 3x/2

Okay so the way my teacher showed me to find a common denominator for all is to do this thing:

4: 2, 2

6: 2, 3

2: 2

Two two's combine to make a single two, so I grabbed the one from 6 and 2. And then you're supposed to times each of the numbers - - > (2)(2)(2)(3) And I got 24, but its supposed to be 12, and why doesnt it work with this process? The way my teacher showed me is supposed to be easy if we encounter with big numbers, hve no idea why it doesnt work for this one:\

Originally posted by: -Ayeshaa-

Addition and Subtraction of Rational Expressions.

Simplify:

x/4 + x+3/6 + 3x/2

Okay so the way my teacher showed me to find a common denominator for all is to do this thing:

4: 2, 2

6: 2, 3

2: 2

Two two's combine to make a single two, so I grabbed the one from 6 and 2. And then you're supposed to times each of the numbers - - > (2)(2)(2)(3) And I got 24, but its supposed to be 12, and why doesnt it work with this process? The way my teacher showed me is supposed to be easy if we encounter with big numbers, hve no idea why it doesnt work for this one:\

Originally posted by: -Ayeshaa-

Thanks so much Akhl, the way you explain things, so understandable :) Thank you!

Consider rectangle shown with area of 24x^3-54x^2-15x with length side of 6x^2-15x. Write and simplify an expression for the length of the rectangle.

Part b to ^ that one. - - - > Determine the perimeter of the rectangle if x = 2V2 cm. Give answer in simplest radical form. (V is symbol for that radical, dont know how to make radical sign on computer)

Originally posted by: priya_94

Hey i need help with math can anyone help me plzz :)...

1). A newspaper delivery person in a car is tossing folded newpapers from the care window to driveways. The speed of the car is 30 feet per second, and the driver does not slow down. The newspapers are tossed horizontally from the height of 4 feet above the ground. The striaght. the height of the newspapers as they are thrown can be modeled by y= -16t^2 + 4. and the distances they travel to the driveway is d= 30t.

A). How long does it take for the newspaper to land?

y = -16 t^2 + 4
When the newspaper lands on the ground, then y = 0
0 = -16 t^2 + 4
16 t^2 = 4
t^2 = 4/16 = 1/4
t = 1/2 = 0.5 second (Answer)

B). From how many feet before the driveway must the papers be throw?

d = 30t = 30 * 0.5 = 15 feet (Answer)

C). The delivery person starts to throw the newspapers at an angle and the height of the papers as they travel can now be modeled by y=-16t^2 +12t +4. How long does it take the papers to reach the ground now?

y = -16 t^2 + 12t + 4
When the newspaper reaches the ground, y = 0
-16 t^2 + 12t + 4 = 0
Dividing both sides by -4
4t^2 - 3t - 1 = 0
(t-1)(4t+1) = 0
t-1 = 0, 4t+1 = 0
t = 1, t = -1/4 (rejected as t cannot be negative)

t = 1 second (Answer)

thnks very much 😃