Question

simplifique as frações algébricas

a) x² - 16 / x² + 5x - 36

b) 2x² - 6x / x² - 8x + 15

c) 3x² - 21 + 36 / 3x² - 27

d) x² - 1 / 5x² + 5x

Answer 1

a) $\frac{ x^{2} -16}{ x^{2} +5x-36}= \frac{(x+4).(x-4)}{(x+9).(x-4)} = \frac{x+4}{x+9}$

b) $\frac{2 x^{2} -6x}{ x^{2} -8x+15} = \frac{2x(x-3)}{(x-5)(x-3)}= \frac{2x}{x-5}$

c) $\frac{3 x^{2} -21+36}{3 x^{2} -27}= \frac{3 x^{2} +15}{3 x^{2} -27}= \frac{3 ( x^{2} +5)}{3( x^{2} -9)} = \frac{ x^{2} +5}{ x^{2} -9}$

d) $\frac{ x^{2} -1}{5 x^{2} +5x} = \frac{(x+1)(x-1)}{5x(x+1)} = \frac{x-1}{5x}$