Question

A)x/7 - x/x-5 б)a+3/a+2 - a+2/a+1 в)3y/y²+4y+4 + 3/y+2 г)b/b-c - b²/b²-c²

Answer 1

Это первое. Сейчас остальное скину

Answer 2

It seems like you've provided some algebraic expressions and you would like me to simplify them. Let's go through each one step by step:

A) x/7 - x/(x-5) To simplify this expression, we need a common denominator. The common denominator is 7(x - 5). So, we'll rewrite the fractions with this common denominator:

x(7x - 35)/(7 * 7x) - 7x/(7x - 35)

Now combine the fractions over the common denominator:

(7x^2 - 35x - 49x)/(7 * 7x)

Combine the like terms in the numerator:

(7x^2 - 84x)/(49x)

Now factor out a 7x from the numerator:

7x(x - 12)/(49x)

Cancel out the common factor of 7x in the numerator and denominator:

(x - 12)/7

B) (a+3)/(a+2) - (a+2)/(a+1) The common denominator here is (a + 1)(a + 2). Rewrite the fractions:

(a + 3)(a + 1)/((a + 1)(a + 2)) - (a + 2)(a + 2)/((a + 1)(a + 2))

Combine the fractions over the common denominator:

(a^2 + 4a + 3 - a^2 - 4a - 4)/((a + 1)(a + 2))

Simplify the numerator:

(-1)/((a + 1)(a + 2))

C) 3y/(y² + 4y + 4) + 3/(y + 2) The first fraction's denominator can be factored as (y + 2)(y + 2) or (y + 2)^2:

3y/((y + 2)^2) + 3/(y + 2)

Now, find a common denominator, which is (y + 2)^2:

(3y + 3(y + 2))/((y + 2)^2)

Combine the numerators:

(3y + 3y + 6)/((y + 2)^2)

Simplify the numerator:

(6y + 6)/((y + 2)^2)

Factor out a common factor of 6 from the numerator:

6(y + 1)/((y + 2)^2)

D) b/(b - c) - b²/(b² - c²) For the second fraction, the denominator can be factored as the difference of squares:

b/(b - c) - b²/((b + c)(b - c))

Now, find a common denominator, which is (b - c)(b + c):

(b(b + c))/((b - c)(b + c)) - b²/((b + c)(b - c))

Combine the fractions over the common denominator:

(b(b + c) - b²)/((b + c)(b - c))

Simplify the numerator:

(b² + bc - b²)/((b + c)(b - c))

Simplify further:

(bc)/((b + c)(b - c))

So, these are the simplified forms of the given expressions:

A) (x - 12)/7 B) -1/((a + 1)(a + 2)) C) 6(y + 1)/((y + 2)^2) D) (bc)/((b + c)(b - c))