Question

Y+6 y+2 5 ___ - ____ + ____ - спростити вираз 4y+8 4y-8 y^2 -4

Answer 1

$\frac{y + 6}{4y + 8} - \frac{y + 2}{4y - 8} + \frac{5}{ {y}^{2} - 4 } = \frac{y + 6}{4(y + 2)} - \frac{y + 2}{4(y - 2)} + \frac{5}{(y - 2)(y + 2)} = \frac{ (y + 6)(y + 2)}{4(y + 2)(y - 2)} - \frac{(y + 2) ^{2} }{4(y - 2)(y + 2)} - \frac{20}{4(y - 2)(y + 2)} = \frac{ {y}^{2} + 6y + 2y + 12 - {y}^{2} - 4y - 4 - 20 }{4(y - 2)( y + 2)} = \frac{4y - 12}{4(y - 2)(y + 2)} = \frac{4(y - 3)}{4(y - 2)(y + 2)} = \frac{y - 3}{(y - 2)(y + 2)}$

Answer 2

To simplify the expression, we need to combine like terms and perform any necessary algebraic operations. Let's start step by step:

1. Combine the fractions on the left side: (Y + 6) / (4y + 8) - (Y + 2) / (4y - 8) + 5

2. Find a common denominator for the fractions: The common denominator for (4y + 8) and (4y - 8) is 4(y + 2)(y - 2).

3. Rewrite the fractions with the common denominator: [(Y + 6)(4y - 8)] / [4(y + 2)(y - 2)] - [(Y + 2)(4y + 8)] / [4(y + 2)(y - 2)] + 5

4. Combine the fractions over the common denominator: [(4y + 24y - 48) - (4y + 8y + 16)] / [4(y + 2)(y - 2)] + 5

5. Simplify the numerator: (28y - 48 - 12y) / [4(y + 2)(y - 2)] + 5

6. Combine like terms in the numerator: (16y - 48) / [4(y + 2)(y - 2)] + 5

7. Factor out the common factor in the numerator: 16(y - 3) / [4(y + 2)(y - 2)] + 5

8. Simplify the fraction: 4(y - 3) / [(y + 2)(y - 2)] + 5

9. Find a common denominator for the whole expression: The common denominator for 4(y - 3) and [(y + 2)(y - 2)] is (y + 2)(y - 2).

10. Rewrite the expression with the common denominator: [4(y - 3) + 5(y + 2)(y - 2)] / [(y + 2)(y - 2)]

11. Expand the second term in the numerator: [4(y - 3) + 5(y^2 - 4)] / [(y + 2)(y - 2)]

12. Distribute the 5 in the numerator: [4y - 12 + 5y^2 - 20] / [(y + 2)(y - 2)]

13. Combine like terms in the numerator: (5y^2 + 4y - 32) / [(y + 2)(y - 2)]

So, the simplified expression is: (5y^2 + 4y - 32) / [(y + 2)(y - 2)]