Comparte esto 👍👍

DESCARGA

CAPITULO XIV

Operaciones con Fracciones

Ejercicio 126

Simplificar:

$\begin{matrix} \frac{x - 2}{4} + \frac{3 x + 2}{6} & = \frac{3 (x - 2) + 2 (3 x + 2)}{12} \\ = \frac{3 x - 6 + 6 x + 4}{12} \\ = \frac{9 x - 2}{12} \end{matrix}$
$\begin{matrix} \frac{2}{5 a^{2}} + \frac{1}{3 a b} & = \frac{2 (3 b) + 5 a}{15 a^{2} b} \\ = \frac{6 b + 5 a}{15 a^{2} b} \end{matrix}$
$\begin{matrix} \frac{a - 2 b}{15 a} + \frac{b - a}{20 b} & = \frac{4 b (a - 2 b) + 3 a (b - a)}{60 a b} \\ = \frac{4 a b - 8 b^{2} + 3 a b - 3 a^{2}}{60 a b} \\ = \frac{- 8 b^{2} + 7 a b - 3 a^{2}}{60 a b} \end{matrix}$
$\begin{matrix} \frac{a + 3 b}{3 a b} + \frac{a^{2} b - 4 a b^{2}}{5 a^{2} b^{2}} & = \frac{a + 3 b}{3 a b} + \frac{a b (a - 4 b)}{5 a^{2} b^{2}} \\ = \frac{5 (a + 3 b) + 3 (a - 4 b)}{15 a b} \\ = \frac{5 a + 15 b + 3 a - 12 b}{15 a b} \\ = \frac{8 a + 3 b}{15 a b} \end{matrix}$
$\begin{matrix} \frac{a - 1}{3} + \frac{2 a}{6} + \frac{3 a + 4}{12} & = \frac{1}{3} [a - 1 + \frac{2 a}{2} + \frac{3 a + 4}{4}] \\ = \frac{1}{3} [a - 1 + a + \frac{3 a + 4}{4}] \\ = \frac{1}{3} [2 a - 1 + \frac{3 a + 4}{4}] \\ = \frac{1}{3} [\frac{4 (2 a - 1) + 3 a + 4}{4}] \\ = \frac{1}{3} [\frac{8 a - 4 + 3 a + 4}{4}] \\ = \frac{1}{3} (\frac{11 a}{4}) \\ \frac{11 a}{12} \end{matrix}$
$\begin{matrix} \frac{n}{m^{2}} + \frac{3}{m n} + \frac{2}{m} & = \frac{1}{m} [\frac{n}{m} + \frac{3}{n} + 2] \\ = \frac{1}{m} [\frac{n^{2} + 3 m + 2 m n}{m n}] \\ = \frac{n^{2} + 2 m n + 3 m}{m^{2} n} \end{matrix}$
$\begin{matrix} \frac{1 - x}{2 x} + \frac{x + 2}{x^{2}} + \frac{1}{3 a x^{2}} & = \frac{1}{x} [\frac{1 - x}{2} + \frac{x + 2}{x} + \frac{1}{3 a x}] \\ = \frac{1}{x} [\frac{3 a x (1 - x) + 6 a (x + 2) + 2}{6 a x}] \\ = \frac{1}{x} [\frac{3 a x - 3 a x^{2} + 6 a x + 12 a + 2}{6 a x}] \\ = \frac{9 a x - 3 a x^{2} + 12 a + 2}{6 a x^{2}} \end{matrix}$
$\begin{matrix} \frac{2 a - 3}{3 a} + \frac{3 x + 2}{10 x} + \frac{x - a}{5 a x} & = \frac{10 x (2 a - 3) + 3 a (3 x + 2) + 6 (x - a)}{30 a x} \\ = \frac{20 a x - 30 x + 9 a x + 6 a + 6 x - 6 a}{30 a x} \\ = \frac{29 a x - 24 x}{30 a x} \\ = \frac{x (29 a - 24)}{30 a x} \\ = \frac{29 a - 24}{30 a} \end{matrix}$
$\begin{matrix} \frac{3}{5} + \frac{x + 2}{2 x} + \frac{x^{2} + 2}{6 x^{2}} & = \frac{3 (6 x^{2}) + 15 x (x + 2) + 5 (x^{2} + 2)}{30 x^{2}} \\ = \frac{18 x^{2} + 15 x^{2} + 30 x + 5 x^{2} + 10}{30 x^{2}} \\ = \frac{38 x^{2} + 30 x + 10}{30 x^{2}} \\ = \frac{2 (19 x^{2} + 15 x + 5)}{x^{2}} \\ = \frac{19 x^{2} + 15 x + 5}{15 x^{2}} \end{matrix}$
$\begin{matrix} \frac{x - y}{12} + \frac{2 x + y}{15} + \frac{y - 4 x}{30} & = \frac{1}{3} [\frac{x - y}{4} + \frac{2 x + y}{5} + \frac{y - 4 x}{10}] \\ = \frac{1}{3} [\frac{5 (x - y) + 4 (2 x + y) + 2 (y - 4 x)}{20}] \\ = \frac{1}{3} [\frac{5 x - 5 y + 8 x + 4 y + 2 y - 8 x}{20}] \\ = \frac{1}{3} [\frac{5 x + y}{20}] \\ = \frac{5 x + y}{60} \end{matrix}$
$\begin{matrix} \frac{m - n}{m n} + \frac{n - a}{n a} + \frac{2 a - m}{a m} & = \frac{a (m - n) + m (n - a) + n (2 a - m)}{a m n} \\ = \frac{a m - a n + m n - a m + 2 a n - m n}{a m n} \\ = \frac{a n}{a m n} \\ = \frac{1}{m} \end{matrix}$
$\begin{matrix} \frac{x + 2}{3 x} + \frac{x^{2} - 2}{5 x^{2}} + \frac{2 - x^{3}}{9 x^{3}} & = \frac{1}{x} [\frac{x + 2}{3} + \frac{x^{2} - 2}{5 x} + \frac{2 - x^{3}}{9 x^{2}}] \\ = \frac{1}{x} [\frac{15 x^{2} (x + 2) + 9 x (x^{2} - 2) + 5 (2 - x^{3})}{45 x^{2}}] \\ = \frac{1}{x} [\frac{15 x^{3} + 30 x^{2} + 9 x^{3} - 18 x + 10 - 5 x^{3}}{45 x^{2}}] \\ = \frac{1}{x} [\frac{19 x^{3} + 30 x^{2} - 18 x + 10}{45 x^{2}}] \\ = \frac{19 x^{3} + 30 x^{2} - 18 x + 10}{45 x^{3}} \end{matrix}$
$\begin{matrix} \frac{1}{a b} + \frac{b^{2} - a^{2}}{a b^{3}} + \frac{a b + b^{2}}{a^{2} b^{2}} & = \frac{1}{a b} + \frac{b^{2} - a^{2}}{a b^{3}} + \frac{b (a + b)}{a^{2} b^{2}} \\ = \frac{1}{a b} [1 + \frac{b^{2} - a^{2}}{b^{2}} + \frac{a + b}{a}] \\ = \frac{1}{a b} [\frac{a b^{2} + a (b^{2} - a^{2}) + b^{2} (a + b)}{a b^{2}}] \\ = \frac{1}{a b} [\frac{a b^{2} + a b^{2} - a^{3} + a b^{2} + b^{3}}{a b^{2}}] \\ = \frac{1}{a b} [\frac{b^{3} + 3 a b^{2} - a^{3}}{a b^{2}}] \\ = \frac{b^{3} + 3 a b^{2} - a^{3}}{a^{2} b^{3}} \end{matrix}$
$\begin{matrix} \frac{a + 3 b}{a b} + \frac{2 a - 3 m}{a m} + \frac{3}{a} & = \frac{1}{a} [\frac{a + 3 b}{b} + \frac{2 a - 3 m}{m} + 3] \\ = \frac{1}{a} [\frac{m (a + 3 b) + b (2 a - 3 m) + 3 b m}{b m}] \\ = \frac{1}{a} [\frac{a m + 3 b m + 2 a b - 3 b m + 3 b m}{b m}] \\ = \frac{1}{a} [\frac{a m + 2 a b + 3 b m}{b m}] \\ = \frac{a m + 2 a b + 3 b m}{a b m} \end{matrix}$