Ejercicio 122 – Solucionario Baldor

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DESCARGA

CAPITULO XIII

Reducción de fracciones
Reducir una fracción a términos mayores

Ejercicio 122

Completar:

$\begin{matrix} \frac{3}{2 a} & = \frac{}{4 a^{2}} \\ 4 a^{2} \div 2 a & = 2 a \\ 3 \times 2 a & = 6 a \\ \frac{6 a}{4 a^{2}} \end{matrix}$
$\begin{matrix} \frac{5}{9 x^{2}} & = \frac{20 a}{} \\ 20 a \div 5 & = 4 a \\ 9 x^{2} \times 4 a & = 36 a x^{2} \\ \frac{20 a}{36 a x^{2}} \end{matrix}$
$\begin{matrix} \frac{m}{a b^{2}} & = \frac{}{2 a^{2} b^{2}} \\ 2 a^{2} b^{2} \div a b^{2} & = 2 a \\ m \times 2 a & = 2 a m \\ \frac{2 a m}{2 a^{2} b^{2}} \end{matrix}$
$\begin{matrix} \frac{3 x}{8 y} & = \frac{9 x^{2} y^{2}}{} \\ 9 x^{2} y^{2} \div 3 x & = 3 x y^{2} \\ 8 y \times 3 x y^{2} & = 24 x y^{3} \\ \frac{9 x^{2} y^{2}}{24 x y^{3}} \end{matrix}$
$\begin{matrix} \frac{4 m}{5 n^{2}} & = \frac{}{5 n^{3}} \\ 5 n^{3} \div 5 n^{2} & = n \\ 4 m \times n & = 4 m n \\ \frac{4 m n}{5 n^{3}} \end{matrix}$
$\begin{matrix} \frac{2 x + 7}{5} & = \frac{}{15} \\ 15 \div 5 & = 3 \\ 3 (2 x + 7) & = 6 x + 21 \\ \frac{6 x + 21}{15} \end{matrix}$
$\begin{matrix} \frac{2 x}{x - 1} & = \frac{}{x^{2} - x} \\ x^{2} - x \div x - 1 & = x (x - 1) \div x - 1 \\ = x \\ x \times 2 x & = 2 x^{2} \\ \frac{2 x^{2}}{x^{2} - x} \end{matrix}$
$\begin{matrix} \frac{a^{2}}{a + 2} & = \frac{2 a^{3}}{} \\ 2 a^{3} \div a^{2} & = 2 a \\ 2 a (a + 2) & = 2 a^{2} + 4 a \\ \frac{2 a^{3}}{2 a^{2} + 4 a} \end{matrix}$
$\begin{matrix} \frac{3 a}{a + b} & = \frac{}{a^{2} + 2 a b + b^{2}} \\ a^{2} + 2 a b + b^{2} \div a + b & = {(a + b)}^{2} \div a + b \\ = a + b \\ 3 a (a + b) & = 3 a^{2} + 3 a b \\ \frac{3 a^{2} + 3 a b}{a^{2} + 2 a b + b^{2}} \end{matrix}$
$\begin{matrix} \frac{x - 4}{x + 3} & = \frac{}{x^{2} + 5 x + 6} \\ x^{2} + 5 x + 6 \div x + 3 & = (x + 3) (x + 2) \div x + 3 \\ = x + 2 \\ (x + 2) (x - 4) & = x^{2} - 2 x - 8 \\ \frac{x^{2} - 2 x - 8}{x^{2} + 5 x + 6} \end{matrix}$
$\begin{matrix} \frac{2 a}{x + a} & = \frac{2 a^{3}}{} \\ 2 a^{3} \div 2 a & = a^{2} \\ a^{2} (x + a) & = a^{2} x + a^{3} \\ \frac{2 a^{3}}{a^{2} x + a^{3}} \end{matrix}$
$\begin{matrix} \frac{x - y}{6} & = \frac{}{12} \\ 12 \div 6 & = 2 \\ 2 (x - y) & = 2 x - 2 y \\ \frac{2 x - 2 y}{12} \end{matrix}$
$\begin{matrix} \frac{5 x}{a - b} & = \frac{}{a^{2} - b^{2}} \\ a^{2} - b^{2} \div a - b & = (a - b) (a + b) \div a - b \\ = a + b \\ 5 x (a + b) & = 5 a x + 5 b x \\ \frac{5 a x + 5 b x}{a^{2} - b^{2}} \end{matrix}$
$\begin{matrix} \frac{x - 5}{a} & = \frac{3 x^{2} - 15 x}{} \\ 3 x^{2} - 15 x \div x - 5 & = 3 x (x - 5) \div x - 5 \\ = 3 x \\ a \times 3 x & = 3 a x \\ \frac{3 x^{2} - 15 x}{3 a x} \end{matrix}$
$\begin{matrix} \frac{5 x}{2 x + y} & = \frac{}{4 x^{2} + 4 x y + y^{2}} \\ 4 x^{2} + 4 x y + y^{2} \div 2 x + y & = {(2 x + y)}^{2} \div 2 x + y \\ = 2 x + y \\ 5 x (2 x + y) & = 10 x^{2} + 5 x y \\ \frac{10 x^{2} + 5 x y}{4 x^{2} + 4 x y + y^{2}} \end{matrix}$
$\begin{matrix} \frac{x + 3}{x + 1} & = \frac{x^{2} - 9}{} \\ x^{2} - 9 \div x + 3 & = (x + 3) (x - 3) \div x + 3 \\ = x - 3 \\ (x + 1) (x - 3) & = x^{2} - 2 x - 3 \\ \frac{x^{2} - 9}{x^{2} - 2 x - 3} \end{matrix}$
$\begin{matrix} \frac{2}{a + 1} & = \frac{}{a^{3} + 1} \\ a^{3} + 1 \div a + 1 & = (a + 1) (a^{2} - a + 1) \div a + 1 \\ = a^{2} - a + 1 \\ 2 (a^{2} - a + 1) & = 2 a^{2} - 2 a + 2 \\ \frac{2 a^{2} - 2 a + 2}{a^{3} + 1} \end{matrix}$
$\begin{matrix} \frac{x - 2 y}{3 x} & = \frac{}{9 x^{2} y} \\ 9 x^{2} y \div 3 x & = 3 x y \\ 3 x y (x - 2 y) & = 3 x^{2} y - 6 x y \\ \frac{3 x^{2} y - 6 x y^{2}}{9 x^{2} y} \end{matrix}$
$\begin{matrix} \frac{x - 1}{x + 1} & = \frac{x^{2} - 1}{} \\ x^{2} - 1 \div x - 1 & = (x - 1) (x + 1) \div x - 1 \\ = x + 1 \\ (x + 1) (x + 1) & = {(x + 1)}^{2} \\ \frac{x^{2} - 1}{{(x + 1)}^{2}} \end{matrix}$
$\begin{matrix} \frac{a - b}{7 a^{2}} & = \frac{}{63 a^{3} b} \\ 63 a^{3} b \div 7 a^{2} & = 9 a b \\ 9 a b (a - b) & = 9 a^{2} b - 9 a b^{2} \\ \frac{9 a^{2} b - 9 a b^{2}}{63 a^{3} b} \end{matrix}$
$\begin{matrix} \frac{x + 1}{x + 5} & = \frac{}{x^{2} + 3 x - 10} \\ x^{2} + 3 x - 10 \div x + 5 & = (x + 5) (x - 2) \div x + 5 \\ = x - 2 \\ (x + 1) (x - 2) & = x^{2} - x - 2 \\ \frac{x^{2} - x - 2}{x^{2} + 3 x - 10} \end{matrix}$