Question

Выполните вычитание:
1) y-8/2y - 3-4y/y^2
2) 7/a - 56/a^2+8a
3) b/b+1 - b^2/b^2-1
4) 3x - 15x^2/5x+2
Заранее спасибо!

Answer 1

1)
$frac{y - 8}{2y} - frac{3 - 4y}{y {}^{2} } = frac{y {}^{2} - 8y - 6 + 8y }{2y {}^{2} } = frac{y {}^{2} - 6}{2y {}^{2} }$
2)
$frac{7}{a} - frac{56}{a {}^{2} + 8a} = frac{7a {}^{2} + 56a - 56a }{a(a {}^{2} + 8a) } = frac{7a {}^{2} }{a {}^{3} + 8a {}^{2} } = frac{7a {}^{2} }{a {}^{2} (a + 8)} = frac{7}{a + 8}$
3)
$frac{b}{b + 1} - frac{b {}^{2} }{b {}^{2} - 1} = frac{b {}^{2} - b - b {}^{2} }{b {}^{2} - 1 } = - frac{b}{b {}^{2} - 1}$
4)
$3x - frac{15x {}^{2} }{5x + 2} = frac{15x {}^{2} + 6x}{5x + 2} - frac{15x {}^{2} }{5x + 2} = frac{15x {}^{2} + 6x - 15x {}^{2} }{5x + 2} = frac{6x}{5x + 2}$