100%

Общая оценка

# номер 97 гдз 8 класс алгебра Муравин Муравин

1)$$\frac{2n+k}{n-k}+\frac{n+2k}{k}$$ $$\frac{2kn+k^{2}+n^{2}-nk+2kn-2k^{2}}{k\left ( n-k \right )}=$$ $$=\frac{3nk-k^{2}+n^{2}}{k\left ( n-k \right )}$$ 2)$$\frac{3b-2c}{b}-\frac{b+c}{b-2c}$$ $$\frac{\left ( b-2c \right )\left ( 3b-2c \right )-b\left ( b+c \right )}{b\left ( b-2c \right )}=$$ $$=\frac{3b^{2}-2bc-6bc+4c^{2}-b^{2}-bc}{b\left ( b-2c \right )}=$$ $$=\frac{2b^{2}-9bc+4c^{2}}{b\left ( b-2c \right )}$$ 3)$$\frac{5}{x-y}-\frac{4}{x+y}$$ $$\frac{5x+5y-4x+4y}{\left ( x-y \right )\left ( x+y \right )}=$$ $$=\frac{x+9y}{\left ( x-y \right )\left ( x+y \right )}$$ 4)$$\frac{9}{2x-y}-\frac{7}{2x+y}$$ $$\frac{18x+9y-14x+7y}{\left ( 2x-y \right )\left ( 2x+y \right )}=$$ $$=\frac{4x+16y}{\left ( 2x-y \right )\left ( 2x+y \right )}$$ 5)$$\frac{5x+3y}{2\left ( x+y \right )}-\frac{7x+4y}{3\left ( x+y \right )}$$ $$\frac{15x+9y-14x-8y}{6\left ( x+y \right )}=$$ $$=\frac{x+y}{6\left ( x+y \right )}=\frac{1}{6}$$ 6)$$\frac{a^{2}}{x\left ( a-x \right )}+\frac{x}{x-a}$$ $$\frac{a^{2}}{x\left ( a-x \right )}-\frac{x}{a-x}=\frac{a^{2}-x^{2}}{x\left ( a-x \right )}=$$ $$=\frac{\left ( a-x \right )\left ( a+x \right )}{x\left ( a-x \right )}=\frac{a+x}{x}$$ 7)$$\frac{11a+13b}{3\left ( a-b \right )}+\frac{15a+17b}{4\left ( b-a \right )}$$ $$\frac{13b+11a}{3\left ( a-b \right )}-\frac{15a+17b}{4\left ( a-b \right )}$$ $$\frac{52b+44a-45a-51b}{12\left ( a-b \right )}=$$ $$=\frac{b-a}{12\left ( a-b \right )}=-\frac{1}{12}$$ 8)$$\frac{8x+14y}{3\left ( 2y-x \right )}+\frac{14x+22y}{5\left ( x-2y \right )}$$ $$\frac{8x+14y}{3\left ( 2y-x \right )}-\frac{14x+22y}{5\left ( 2y-x \right )}$$ $$\frac{40x+70y-42x-66y}{15\left ( 2y-x \right )}=$$ $$=\frac{4y-2x}{15\left ( 2y-x \right )}=\frac{2\left ( 2y-x \right )}{15\left ( 2y-x \right )}=\frac{2}{15}$$ 9)$$\frac{17a-13b}{4\left ( a-b \right )}+\frac{16b-21a}{5\left ( a-b \right )}$$ $$\frac{85a-65b+64b-84a}{4\left ( a-b \right )}=$$ $$=\frac{a-b}{4\left ( a-b \right )}=\frac{1}{4}$$ 10)$$\frac{4y}{b-2y}-\frac{b^{2}-4by}{y\left ( 2y-b \right )}$$ $$\frac{4y}{b-2y}+\frac{b^{2}-4by}{y\left ( b-2y \right )}=$$ $$=\frac{4y^{2}+b^{2}-4by}{y\left ( b-2y \right )}=$$ $$=\frac{\left ( b-2y \right )^{2}}{y\left ( b-2y \right )}=\frac{b-2y}{y}$$ 11)$$\frac{x+4y}{2x\left ( x+y \right )}-\frac{y-4x}{2x\left ( y-x \right )}$$ $$\frac{\left ( -x+y \right )\left ( x+4y \right )-\left ( x+y \right )\left ( y-4x \right )}{2x\left ( x+y \right )\left ( y-x \right )}$$ $$\frac{\left ( y-x \right )\left ( x+4y \right )-\left ( y-4x \right )\left ( x+y \right )}{2x\left ( x+y \right )\left ( y-x \right )}$$ $$\frac{xy+4y^{2}-x^{2}-4xy-yx-y^{2}+4x^{2}+4xy}{2x\left ( x+y \right )\left ( y-x \right )}=$$ $$\frac{3y^{2}+3x^{2}}{2x\left ( y^{2}-x^{2} \right )}=\frac{3\left ( x^{2}+y^{2} \right )}{2x\left ( y^{2}-x^{2} \right )}$$ 12)$$\frac{an-bk}{2nk\left ( k+n \right )}+\frac{an+bk}{2nk\left ( k-n \right )}$$ $$\frac{\left ( k-n \right )\left ( an-bk \right )+\left ( k+n \right )\left ( an+bk \right )}{2nk\left ( k+n \right )\left ( k-n \right )}=$$ $$=\frac{ank-bk^{2}-an^{2}-bnk+ank+bk^{2}+an^{2}+nbk}{2nk\left ( k+n \right )\left ( k-n \right )}=$$ $$=\frac{2abk}{2nk\left (k^{2}-n^{2} \right )}=\frac{a}{k^{2}-n^{2}}$$