Alan

Then we have 4/x + 2 + 1/x - 2 = (5x - 6)/(x² - 4)  and we must have x≠0, x≠2, x≠-2

5/x = (5x - 6)/(x² - 4)

Multiply both sides by (x² - 4)*x

5(x² - 4) = (5x - 6)x

5x² - 20 = 5x² - 6x

-20 = -6x

x = 20/6

x = 10/3

$$x=3\frac{1}{3}$$

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density is mass divided by volume.

If mass = M kg; length = u mm = 10^-3u m;  width = w mm = 10^-3w m;  height = v mm = 10^-3v m; then

density = 10⁹*M/(u*v*w)  kg/m³

Is the first term  $$\frac{4}{x}+2$$  or $$\frac{4}{x+2}$$ ?

Is the second term  $$\frac{1}{x}-2$$  or  $$\frac{1}{x-2}$$  ?

pi has an infinite number of digits!

h = -16t² + 30t + 25  height

v = -32t + 30             velocity

a. Maximum height occurs when v = 0; i.e. when 0 = -32t + 30; t = 30/32; t = 15/16 secs.

b. Height at this time: h = -16*(15/16)² + 30*15/16 + 25 feet; h = 625/16 feet; h ≈ 39 feet

16a²b - 24ab²

The value common to both terms is 8ab so 16a²b - 24ab² can be written as 8ab*(2b - 3a)

I'm guessing you want to factor this.

Look for two numbers that multiply together to make +9 and that added together make -10.

Factors of 9 are 1, 3, and 9.  The product of 1 and 9 is 9; the sum of 1 and 9 is 10.  However, we want the sum to be -10, so we need to have -1 and -9:

(x - 1)*(x - 9) = x² - 10x + 9

Expand the terms and simplify:

First term:   (x + 3)³ = x³ +9x² + 27x + 27

2nd term:    (3x - 1)² = 9x² - 6x + 1

Subtract the second from the first:   x³ + 33x + 26

This must equal: x³ + 4 so

 x³ + 33x + 26 = x³ + 4

33x + 26 = 4

33x = -22

x = -22/33 = -2/3

Check:

$${\left({\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}^{{\mathtt{3}}}{\mathtt{\,-\,}}{\left({\mathtt{\,-\,}}{\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}^{{\mathtt{2}}} = {\frac{{\mathtt{100}}}{{\mathtt{27}}}} = {\mathtt{3.703\: \!703\: \!703\: \!703\: \!703\: \!7}}$$

$${{\mathtt{\,-\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}} = {\frac{{\mathtt{100}}}{{\mathtt{27}}}} = {\mathtt{3.703\: \!703\: \!703\: \!703\: \!703\: \!7}}$$

Ok.

At constant speed the net force on the sled is zero (Newton's 1st law of motion).  The frictional force is given by μ*weight where μ is the coefficient of friction.

μ*52 = 36

μ = 36/52

μ ≈ 0.692