Pojednostavite (x-2) / (x ^ 2 + 6x + 9) - (x + 2) / (2x ^ 2-18)?

Odgovor:

# (X ^ 2-15x + 6) / (2 (x-3) (x + 3) ^ 2) *

Obrazloženje:

# X ^ 2 + 6x + 9 = (x + 3) (x + 3) = (x + 3) ^ 2 #

# 2 x ^ 2-18-2 (x ^ 2-9) = 2 (x-3), (x + 3) *

Razlika od 2 kvadrata # (A-b) (a + b) = a ^ 2-b ^ 2 #

# (X-2) / (x + 3) ^ 2- (x + 2) / (2 (x-3) (x + 3)) *

Pomnožiti sa # 2 (x-3), (x + 3) ^ 2 #

= # ((X-2) (2) (x-3) - (x + 2) (x + 3)) / (2 (x-3) (x + 3) ^ 2) *

Proširite zagrade

= # (2 (x ^ 2-5x + 6) - (x ^ 2 + 5x + 6)) / (2 (x-3) (x + 3) ^ 2) *

Dalje proširite zagrade

= # (2x ^ 2-10x + 12 x ^ 2-5x-6) / (2 (x-3) (x + 3) ^ 2) *

Pojednostaviti

= # (X ^ 2-15x + 6) / (2 (x-3) (x + 3) ^ 2) *

Pojednostavite (1 - cos theta + sin theta) / (1+ cos theta + sin theta)?

= sin (theta) / (1 + cos (theta)) (1-cos (theta) + sin (theta)) / (1 + cos (theta) + sin (theta)) = (1-cos (theta) + sin (theta)) * (1 + cos (theta) + sin (theta)) / (1 + cos (theta) + sin (theta)) ^ 2 = ((1 + sin (theta)) ^ 2-cos 2 (theta)) / (1 + cos ^ 2 (theta) + sin ^ 2 (theta) +2 sin (theta) +2 cos (theta) + 2 sin (theta) cos (theta)) = ((1+ sin (theta)) ^ 2-cos ^ 2 (theta)) / (2 + 2 sin (theta) +2 cos (theta) + 2 sin (theta) cos (theta)) = ((1 + sin (theta)) ) ^ 2-cos ^ 2 (theta)) / (2 (1 + cos (theta)) + 2 sin (theta) (1 + cos (theta)) = (1/2) ((1 + sin (theta)) ) ^ 2-cos ^ 2 (theta)) / ((1 + cos (theta)) (1 + sin (

Pomnožite zagrade i pojednostavite (2sqrta-3sqrtb) (sqrta + sqrtb)?

2a-sqrt (ab) -3b (2sqrt-3sqrt b) (sqrt a + sqrt b) (2sqrta * sqrta) -3sqrtb * sqrta) + (2sqrta * sqrtb) - (3sqrtb * sqrtb) = 2a-3sqrt (ab ) + 2sqrt (ab) -3b = 2a-sqrt (ab) -3b

Kako pojednostavite ((x ^ 2-y ^ 2) (x ^ 2 + xy + y ^ 2)) / ((x ^ 3-y ^ 3) (x ^ 2 + 2xy + y ^ 2))?

To pojednostavljuje na 1 / (x + y). Prvo, faktor donjih desnih i gornjih lijevih polinoma pomoću posebnih binomnih slučajeva faktoringa: boja (bijela) = (boja (zelena) ((x ^ 2-y ^ 2)) (x ^ 2 + xy + y ^ 2)) / ((x ^ 3-y ^ 3) boja (plava) ((x ^ 2 + 2xy + y ^ 2))) = (boja (zelena) ((xy) (x + y)) (x ^ 2 + xy + y ^ 2)) / ((x ^ 3-y ^ 3) boja (plava) ((x + y) (x + y))) Poništite zajednički faktor: = (boja (zelena) ((xy) boja (crvena) cancelcolor (zeleno) ((x + y))) (x ^ 2 + xy + y ^ 2)) / ((x ^ 3-il ^ 3) boja (plava) ((x + y) Boja (crveno) poništavanje boje (plavo) ((x + y)))) = (boja (zelena) ((xy)) (x ^ 2 + xy + y ^ 2)) / ((x ^