Question

50 .

1. сократите дробь:

а) 14b^3/49b ; б) x^2-16/x^3-16; в) y^2-2y+1/1-y^2 .

2. дробь:

а ) x/2y^2 к знаменателю 4xy^3

б)5/m-n к знаменателю m^2-n^2

в)x/3x-3y к знаменателю 3x^2-6xy+3y^2

1. сократите дробь:

а) 16b^2/20b^4 ; б) 4x-12/x^2-9; в) 4-y^2/y^2-4y+4 .

2. дробь:

а ) m/3n^3 к знаменателю 9mn^4

б) 3/x+y к знаменателю x^2-y^2

в) m/2m+2n к знаменателю 2m^2+4mn+2n^2

Answer 1

$1)\; \; \frac{14\, b^3}{49\, b}=\frac{2\, b^2}{7}\; \; ;\\\\\frac{x^2-16}{x^3-64}=\frac{(x-4)(x+4)}{(x-4)(x^2+4x+16)}=\frac{x+4}{x^2+4x+16}\; ;\\\\\frac{y^2-2y+1}{1-y^2}=\frac{(1-y)^2}{(1-y)(1+y)}=\frac{1-y}{1+y}\; ;$

$2)\; \; \frac{x}{2y^2}=\frac{x\, \cdot \, 2xy}{2y^2\, \cdot 2xy}=\frac{2\, x^2\, y}{4\, x\, y^3}\; \; ;\\\\\frac{5}{m-n}=\frac{5\, (m+n)}{(m-n)(m+n)}=\frac{5\, (m+n)}{m^2-n^2}\; ;\\\\\frac{x}{3x-3y}=\frac{x}{3(x-y)}=\frac{x(x-y)}{3(x-y)(x-y)}=\frac{x(x-y)}{3(x-y)^2}=\frac{x(x-y)}{3(x^2-2xy+y^2)}=\frac{x(x-y)}{3x^2-6xy+3y^2}\; ;$

$3)\; \; \frac{16\, b^2}{20\, b^4}=\frac{4}{5\, b^2}\; ;\\\\\frac{4x-12}{x^2-9}=\frac{4\, (x-3)}{(x-3)(x+3)}=\frac{4}{x+3}\; ;\\\\\frac{4-y^2}{y^2-4y+4}=\frac{(2-y)(2+y)}{(2-y)^2}=\frac{2+y}{2-y}\; .$

$4)\; \; \frac{m}{3n^3}=\frac{m\, \cdot \, 3mn}{3n^3\, \cdot \, 3mn}=\frac{3m^2n}{9mn^4}\; ;\\\\\frac{3}{x+y}=\frac{3\, (x-y)}{(x+y)(x-y)}=\frac{3\, (x-y)}{x^2-y^2}\; ;\\\\\frac{m}{2m+2n}=\frac{m}{2(m+n)}=\frac{m(m+n)}{2(m+n)^2}=\frac{m(m+n)}{2(m^2+2mn+n^2)}=\frac{m(m+n)}{2m^2+4mn+2n^2}\; .$