Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 34

а) 15a² − 10ab/3ab − 2b² = 5a(3a − 2b)/b(3a − 2b) = 5a(3a − 2b) : (3a − 2b)/b(3a − 2b) : (3a − 2b) = 5a/b
если a = −2, b = −0,1, то 5a/b = 5 ⋅ (−2)/−0,1 = −10/−0,1 = 100
б) 9c² − 4d²/18c²d − 12cd² = (3c)² − (2d)²/6cd(3c − 2d) = (3c − 2d)(3c + 2d)/6cd(3c − 2d) = (3c − 2d)(3c + 2d) : (3c − 2d)/6cd(3c − 2d) : (3c − 2d) = 3c + 2d/6cd
если c = 2/3, d = 1/2 то 3c + 2d/6cd = $$ \frac{3 \cdot \frac{2}{3}+2 \cdot \frac{1}{2}}{6 \cdot \frac{2}{3} \cdot \frac{1}{2}} $$ = 2 + 1/2 = 3/2 = 1,5
в) 6x² + 12xy/5xy + 10y² = 6x(x + 2y)/5y(x + 2y) = 6x(x + 2y) : (x + 2y)/5y(x + 2y) : (x + 2y) = 6x/5y
если x = 2/3, y = −0,4 то 6x/5y = $$ \frac{6 \cdot \frac{2}{3}}{5 \cdot(-0,4)} $$ = 2 ⋅ 2/−2 = −2
г) x² + 6xy + 9y²/4x² + 12xy = (x + 3y)²/4x(x + 3y) = (x + 3y)(x + 3y) : (x + 3y)/4x(x + 3y) : (x + 3y) = x + 3y/4x
если x = −0,2, y = −0,6, то
x + 3y/4x = −0,2 + 3 ⋅ (−0,6)/4 ⋅ (−0,2) = −0,2 − 1,8/−0,8 = −2/−0,8 = −20/−8 = −20 : 4/−8 : 4 = 5/2 = 2,5