CPhill

Factoring the polynomial - without the leading fraction - we have

x^2 (x + 2) - 2(x + 2) =

(x^2 - 2) (x + 2)

So we have

A = (1/2)(b)(h) =

A =  (1/2)  (x^2 - 2 ) (x + 2)

So the base is represented by

(x^2 - 2)

Factoring the polynomial representing the area before the construction, we have

(x + 2) (x +1)   So the length was (x + 2) and the width was (x + 1)

Factoring the polynomial representing the area after the construction, we have

(x + 3) (x + 5)  So the length was (x + 3) and the width was (x + 5)

So the length increased by 1 and the width increased by 4

Area = pi * (radius)²

OK...so we have

(12 + x) / x = 4 / 3

And taking the cross-product, we have

3 (12 + x) = 4x    Expand the left side   

36 + 3x = 4x       Subtract 3x from both sides

36 = x

And that's it......make sure to check your answer !!

Could you be more specific?? An example of what you're referring to???

So we have  4*10^12 / 5*10^8 =

(4/5) (10^4) =

(.8 ) ( 10^4) =

8000 times

Did you finish your question??

3x minus what ??

Note that, for example,  2^-7   =   1 / 2⁷  = 1 / 128

So we can always write ("1") over (our number raised to the same positive exponent.)

Of course, a calculator can be used, too !!!!

So we have this:

12.6 / x = 17.1 / 11.4

So....by cross-product equality, we have

17.1 * x  = 12.6 * 11.4

17.1 x = 143.64

x = 8.4

Thanks, Alan...I haven't seen that one before....another tool for my chest !!

For some reason...this technique  - to my knowledge -isn't covered in Algebra in the States.....it should be!!

Thums Up from me !!

That's what I like about this site......something new to learn for evetyone!!!