Question

(x/x^2-14x+49) + (x+1/49-x^2)= (y+6/4y+8) - (y+2/4y-8) + (5/y^2-4)= (6b^3+48b/b^3+64) - (3b^2/b^2-46+16)=

Answer 1

Тут необходимо применить формулы сокращенного умножения, их лучше выучить, пригодятся в дальнейшем обучении)))

Answer 2

To simplify the given expressions, let's take one at a time:

1. (x/(x^2 - 14x + 49)) + ((x + 1)/(49 - x^2))

First, factor the denominators: x^2 - 14x + 49 = (x - 7)(x - 7) = (x - 7)^2 49 - x^2 = (7 - x)(7 + x) = -(x - 7)(x + 7)

Now, rewrite the expression with the common denominator, which is (x - 7)^2 * (x + 7): (x/(x^2 - 14x + 49)) + ((x + 1)/(49 - x^2)) = (x/(x - 7)^2) + ((x + 1)/-(x - 7)(x + 7))

To add these fractions, find a common denominator, which is (x - 7)^2 * (x + 7): x(x + 7)/((x - 7)^2 * (x + 7)) - (x + 1)(x - 7)/((x - 7)^2 * (x + 7))

Combine the numerators: (x^2 + 7x - x^2 + 7x - 7)/(x^2 - 14x + 49)

Simplify the expression: (14x - 7)/(x^2 - 14x + 49)

2. (y + 6)/(4y + 8) - (y + 2)/(4y - 8) + 5/(y^2 - 4)

First, factor the denominators: 4y + 8 = 4(y + 2) 4y - 8 = 4(y - 2) y^2 - 4 = (y - 2)(y + 2)

Now, rewrite the expression with the common denominator, which is 4(y + 2)(y - 2): (y + 6)/(4y + 8) - (y + 2)/(4y - 8) + 5/(y^2 - 4) = (y + 6)/(4(y + 2)) - (y + 2)/(4(y - 2)) + 5/((y - 2)(y + 2))

To add these fractions, find a common denominator, which is 4(y + 2)(y - 2): (y + 6)(y - 2)/[4(y + 2)(y - 2)] - (y + 2)(y + 2)/[4(y + 2)(y - 2)] + 20/[(y - 2)(y + 2)]

Combine the numerators: (y^2 + 4y - 2y - 12 - y^2 - 4y - 2y - 4 + 20)/[4(y + 2)(y - 2)]

Simplify the expression: (12 - 4)/[4(y + 2)(y - 2)] 8/[4(y + 2)(y - 2)] 2/[y^2 - 4]

3. (6b^3 + 48b)/(b^3 + 64) - (3b^2)/(b^2 - 46 + 16)

First, factor the denominators: b^3 + 64 = (b + 4)(b^2 - 4b + 16) b^2 - 46 + 16 = (b - 4)(b - 4)

Now, rewrite the expression with the common denominator, which is (b + 4)(b^2 - 4b + 16)(b - 4): (6b^3 + 48b)/(b^3 + 64) - (3b^2)/(b^2 - 46 + 16) = (6b^3 + 48b)/[(b + 4)(b^2 - 4b + 16)] - (3b^2)/[(b - 4)(b - 4)]

To add these fractions, find a common denominator, which is (b + 4)(b^2 - 4b + 16)(b - 4): (6b^3 + 48b)(b - 4)/[(b + 4)(b^2 - 4b + 16)(b - 4)] - 3(b + 4)(b^2 - 4b + 16)/[(b + 4)(b^2 - 4b + 16)(b - 4)]

Combine the numerators: (6b^4 - 24b^3 + 48b^2 - 192b - 3b^3 - 12b^2 + 48b + 192)/[(b + 4)(b^2 - 4b + 16)(b - 4)]

Simplify the expression: (6b^4 - 27b^3 + 36b^2)/[(b + 4)(b^2 - 4b + 16)(b - 4)]