The Greeks started making the Columns while building temples. They started with the Doric, then advanced to the Ionic and later the Corinthian Columns. These architectural designs are used widely today in the construction of storey buildings and other sructures.

Explanation:

3 0

2 years ago

(x+1/x-1 - x-1/x+1 - 4x/x^2 +1) + 4x/x^4-1

Lunna [17]

Answer:

$\frac{12x}{x^4-1}$

Explanation:

Given

$(\frac{x+1}{x-1} - \frac{x-1}{x+1} - \frac{4x}{x^2 + 1}) + \frac{4x}{x^4 - 1}$

Required

Solve:

Take L.C.M of the first two fractions

$(\frac{(x+1)(x+1)-(x-1)(x-1)}{(x-1)(x+1)} - \frac{4x}{x^2 + 1}) + \frac{4x}{x^4 - 1}$

$(\frac{(x+1)(x+1)-(x-1)(x-1)}{x^2-1} - \frac{4x}{x^2 + 1}) + \frac{4x}{x^4 - 1}$

$(\frac{x^2+2x+1-(x^2-2x+1)}{x^2-1} - \frac{4x}{x^2 + 1}) + \frac{4x}{x^4 - 1}$

$(\frac{x^2+2x+1-x^2+2x-1}{x^2-1} - \frac{4x}{x^2 + 1}) + \frac{4x}{x^4 - 1}$

Collect Like Terms

$(\frac{x^2-x^2+2x+2x+1-1}{x^2-1} - \frac{4x}{x^2 + 1}) + \frac{4x}{x^4 - 1}$

$(\frac{4x}{x^2-1} - \frac{4x}{x^2 + 1}) + \frac{4x}{x^4 - 1}$

Solve the expression in bracket

$(\frac{4x(x^2+1) - 4x(x^2-1)}{(x^2-1)(x^2+1)} ) + \frac{4x}{x^4 - 1}$

$(\frac{4x(x^2+1) - 4x(x^2-1)}{x^4-1} ) + \frac{4x}{x^4 - 1}$

$(\frac{4x^3+4x - 4x^3+4x)}{x^4-1} ) + \frac{4x}{x^4 - 1}$

$(\frac{4x^3- 4x^3+4x +4x)}{x^4-1} ) + \frac{4x}{x^4 - 1}$

$\frac{8x}{x^4-1} + \frac{4x}{x^4 - 1}$

Take LCM

$\frac{8x+4x}{x^4-1}$

$\frac{12x}{x^4-1}$

<em>The expression can not be further simplified</em>

7 0

2 years ago

Who are the only people who may introduce a bill in the House of Representatives

Anettt [7]

Representatives introduce bills in the House of Representatives. Ideas can come from basically anyone (citizens). Once the bill is introduced then a clerk will give it a number and then another clerk (reading clerk) will read the bill(s) to the representatives. Then the bill goes to a standing committee ( a committee in the House or Senate that will consider bills in a certain subject area).

7 0

3 years ago

Choose the word or phrase that best completes each of the following sentences.

kotegsom [21]

Answer:

A. Intimidation

Explanation:

3 0

3 years ago