Question

Помогите пожалуйста дам 35 баллов 1) (1/m-n - 1/m+n) : 2/3m-3n = 2) x+y/y * (x/x+y - x-y/x) = 3) (4a - 2a/a+1) * a+1/2а во второй степени 4) 3а-12/a во второй степени * ax-a/4-a + 1-x/2a / -- это в столбик значит а не деление во второй степени не все а а только две во 3 и 4 заранее спасибо

Answer 1

$\displaystyle\bf\\1)\\\\\Big(\frac{1}{m-n}-\frac{1}{m+n} \Big):\frac{2}{3m-3n} =\frac{m+n-m+n}{(m-n)(m+n)} \cdot\frac{3\cdot(m-n)}{2} =\\\\\\=\frac{2n}{m+n} \cdot\frac{3}{2} =\frac{3n}{m+n} \\\\\\2)\\\\\frac{x+y}{y} \cdot\Big(\frac{x}{x+y} -\frac{x-y}{x} \Big)=\frac{x+y}{y} \cdot\frac{x^{2}-(x+y)(x-y) }{x(x+y)} =\\\\\\=\frac{x+y}{y} \cdot\frac{x^{2}-x^{2} +y^{2} }{x(x+y)} =\frac{x+y}{y}\cdot\frac{y^{2} }{x(x+y)} =\frac{y}{x}$

$\displaystyle\bf\\3)\\\\\Big(4a-\frac{2a}{a+1} \Big)\cdot\frac{a+1}{2a^{2} } =\frac{4a^{2} +4a-2a}{a+1} \cdot\frac{a+1}{2a^{2} } =\frac{4a^{2}+2a }{2a^{2} } =\\\\\\=\frac{2a(2a+1)}{2a^{2} } =\frac{2a+1}{a} \\\\\\4)\\\\\frac{3a-12}{a^{2} } \cdot\frac{ax-a}{4-a} +\frac{1-x}{2a} =\Big(\frac{3(a-4)}{a^{2} } \cdot\frac{a(x-1)}{-(a-4)} \Big)+\frac{1-x}{2a} =\\\\\\=\frac{3\cdot(1-x)}{a} +\frac{1-x}{2a} =\frac{6-6x+1-x}{2a} =\frac{7-7x}{2a}$

Answer 2

1) (1/m-n - 1/m+n) / (2/3m-3n) = First, let's find a common denominator for the fractions in the numerator: (1/m-n - 1/m+n) = ((1/m-n)(m+n) - (1/m+n)(m-n)) / (m-n)(m+n) = (m+n - m+n) / (m^2 - n^2) = 0 / (m^2 - n^2) = 0

Now, we can divide by the fraction in the denominator: 0 / (2/3m-3n) = 0

Therefore, the answer is 0.

2) x+y/y * (x/x+y - x-y/x) = First, let's simplify the expression inside the parentheses: (x/x+y - x-y/x) = (x^2 - xy - x^2 + y^2) / (xy(x+y)) = (y^2 - xy) / (xy(x+y)) = y(y-x) / (xy(x+y))

Now, we can multiply by the first fraction: x+y/y * (y(y-x) / (xy(x+y))) = (x+y)(y-y+x) / (xy(x+y)) = xy / (xy(x+y)) = 1 / (x+y)

Therefore, the answer is 1 / (x+y).

3) (4a - 2a/a+1) * a+1/2a = First, let's simplify the expression inside the parentheses: (4a - 2a/a+1) = 2a / (a+1)

Now, we can multiply by the second fraction: 2a / (a+1) * a+1/2a = 2a(a+1) / (a+1)(2a) = 2a / 2a = 1

Therefore, the answer is 1.

4) 3a-12/a^2 * ax-a/4-a = First, let's simplify the expression inside the parentheses and the denominator: (3a-12/a^2) * (ax-a/4-a) = (3(a-4) / a^2) * (a(x-1) / (4-a))

Now, we can cancel out common factors: (3(a-4) / a^2) * (a(x-1) / (4-a)) = 3(x-1) / a(4-a)

Therefore, the answer is 3(x-1) / a(4-a).

I hope this helps! Let me know if you have further questions.