EVALUACION 2

Resuelve las siguientes sumas de fracciones algebraicas con denominador polinomio.

Escribir el desarrollo paso a paso.

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

2. = 2(x-3) +1(x-3)/(x+4)(x-3) = 2x-6+x-3/x²+4x-3x-12 = 3x-9/x²+x-12

3. = 3(2x+5) + 6(1-x) /(1-x)(2x+5) = 6x+15+6-6x/(1-x) (2x+5) = 21 / (1-x) (2x+5)

4. = x(x+y) + x(x-y) / (x-y) (x+y) = x²+xy+x²-xy/ (x-y) (x+y) = 2x² (x-y) (x+y)

5. = (m-2)(m+3) + (m-3)(m+2)/(m-3)(m-2) = m²-2m+3m-6+m²-3m+3m-6/(m—3) (m-2) = 2m²-12/ (m-3) (m-2)

6. = (x+y) (x+y) + (x-y) (x-y) /(x-y) (x+y) = x²+xy+xy+y²+x²-xy-xy+y²/(x-y)(x+y) =

2x²+y²/(x-y) (x+y)

7. = x(x-1) +(x+1) (x+1) / (x-1)² (x+1) = x²-x+x²+x+x+1 = 2x²+x+1/(x-1)²(x+1)

8. = 2(x+5) +1(3x) / (x-5) (x+5) = 2x+10+3x /(x-5) (x+5) = 5x+10/ (x-5) (x+5)

9. = 1(3x+2y) + 1(x-y) / (3x+2y) (3x-2y) = 3x+2y+x-y = 4x-y/ (3x+2y)(3x-2y)

10. (x+a) (x-3a) +1(3a²-x²) / (x+3a) (x-3a) = x²+ax-3ax-3a² +3a²-x² = -2ax/(x+3a) (x-3 a)

11. = a +a/ (1-a) (1+a) (1+a)² = a(1+a)² + a(1-a)² /(1-a)(1+a) (1+a)² =

2a/ (1-a)(1+a)(1+a)²

12. = 2b(a+b) +2a(a-b) /a(a-b) b(a+b) = 2ab+2b²+2a²-2ab = 2b²+2a²/a(a-b) b(a+b)