I have not done this in advance. I'm just going to write it down
and see what I can do with it:
[ 1/(x+3)² - 1/x² ] / 3
Multiply the top and bottom by (x+3)² :
[ 1 - (x+3)²/x² ] / 3 (x+3)²
Multiply the top and bottom by x² :
[ x² - (x+3)² ] / 3 x² (x+3)²
Now it's just a matter of expanding and cleaning things up,
and hope and pray that a lot of things cancel.
Eliminate the parentheses on top and bottom:
[ x² - x² - 6x -9 ] / 3 x² (x² + 6x + 9)
Combine the x² terms on top, and divide top and bottom by 3 :
[ - 2x - 3 ] / x² (x² + 6x + 9)
Finally, all I can make of this is:
- (2x + 3) / [ x(x+3) ]² .
That's not a whole lot prettier than the original form, but at least
we got rid of those fractions in the numerator of a fraction.
I hope this is some help to you.
Answer:
The ratio of the length of DE and the length of BC = 1/4
Step-by-step explanation:
From the figure we can see two sectors
<u>To find the length of BC</u>
The sector ABC with radius r and central angle 2β
BC = (2πr)( 2β/360)
= 4πrβ/360
<u>To find the length of DE</u>
The sector ADE with radius r/2 and central angle β
DE = (2πr/2)( β/360)
= πrβ/360
<u>To find the ratio of DE to BC</u>
DE/BC =πrβ/360 ÷ 4πrβ/360
= πrβ/360 * 360/ 4πrβ
=1/4
4(x + 2) = 48
4x + 8 = 48 |subtract 8 from both sides
4x = 40 |divide both sides by 4
x = 10
Examples of rational numbers :
1, 1/2, 3/4 , 5 , 6, 15/8 etc
Rational numbers are numbers which can be written as fraction as also that the numerator and denominator are whole examples.
Example 5 can be written as fraction in the form of 5/1.