Question

Simplifique as frações algébricas:
a)x²-10x+25/x²-25
b)ax+bx-ay-by/a²-b²
c)a²-3a/a²-6a+9
d)3x²y-3x²y/x²-2xy+y²
e)25a²+30ab+9b²/25a²-9b²
URGENTE É PRA HJ!!!!!!!!!!!!

Answer 1

Explicação passo-a-passo:

a)

$\sf \dfrac{x^2-10x+25}{x^2-25}$

$\sf =\dfrac{(x-5)\cdot(x-5)}{(x-5)\cdot(x+5)}$

$\sf =\red{\dfrac{x-5}{x+5}}$

b)

$\sf \dfrac{ax+bx-ay-by}{a^2-b^2}$

$\sf =\dfrac{x\cdot(a+b)-y\cdot(a+b)}{(a+b)\cdot(a-b)}$

$\sf =\dfrac{(a+b)\cdot(x-y)}{(a+b)\cdot(a-b)}$

$\sf =\red{\dfrac{x-y}{a-b}}$

c)

$\sf \dfrac{a^2-3a}{a^2-6a+9}$

$\sf =\dfrac{a\cdot(a-3)}{(a-3)\cdot(a-3)}$

$\sf =\red{\dfrac{a}{a-3}}$

d)

$\sf \dfrac{3x^2y-3xy^2}{x^2-2xy+y^2}$

$\sf =\dfrac{3xy\cdot(x-y)}{(x-y)\cdot(x-y)}$

$\sf =\red{\dfrac{3xy}{x-y}}$

e)

$\sf \dfrac{25a^2+30ab+9b^2}{25a^2-9b^2}$

$\sf =\dfrac{(5a+3b)\cdot(5a+3b)}{(5a+3b)\cdot(5a-3b)}$

$\sf =\red{\dfrac{5a+3b}{5a-3b}}$