Simplifying Radicals and Rationals?

Question

Simplify:
(4) / ( x+5) - (6x - 1) / (x^2 + 10x + 25)

Simplify:
(5) / (x) + (x + 1) / (x + 2) = (2x + 9) / (x + 2)

My teacher doesn't teach well or rather, at all, so any help at all would be greatly appreciated.

Answer 1

= (x + 5) - (6x - 1) / (x² + 10x + 25)

Consider  x² + 10x + 25.

Now solve the factor method.

Look at the product of the first and last coefficients: (1)(25) = 25.

We want two factors of 25 whose sum middle coefficient of 10, and they are 5 and 5.

= x² + 5x + 5x + 25.

= x(x + 5) + 5(x + 5)

Take out common factors.

= (x + 5)(x + 5)

= (x + 5)²

(x + 5) - (6x - 1) / (x² + 10x + 25) = (x + 5 - 6x + 1) / (x + 5)²

=  (6 - 5x) / (x + 5)².

Answer 2

(x) + (x + 1) / (x + 2) = (2x + 9) / (x + 2)

Rewrite the expression with common denominator.

[(x)(x + 2) + (x + 1)] / (x + 2) = (2x + 9) / (x + 2)

Multiply each side by (x + 2).

X² + 2x + x + 1 = (2x + 9) Subtract (2x + 9) from each side.

(X² + 2x + x + 1) - (2x + 9) = (2x + 9) - (2x + 9).

x² + x -8 = 0

Now solve the factor method.

Comapre equation with standard from ax²+bx+c=0 and write the coefficients.

Recall Quadratic formula: x =[ -b + √(b² - 4ac)]/2a

Substitute a = 1, b = 1 and c = -8 in the equation.

x = [-1+ √[(1)² - 4(1)(-8)]] / 2(1)

x = [-1+ √[1 + 32]] / 2

x = [-1+ √[33]] / 2

x = [-1+ √[33]] / 2 or x = [-1+ √33] / 2.