Practice

Presentation

\frac{1}{y} - \frac{1}{y - 3}

y(y-3)

-3/y(y-3) Y not 0,3

\frac{6}{2 x + 4} - \frac{5 - x}{2 x + 4}

$\frac{x + 1}{2 x + 1}$ x cant be -2

\frac{4 a - 3}{2 a - 1} - \frac{7}{a + 3} \frac{4 a ^{2} - 3 a}{2 a ^{2} - a} - \frac{7 a}{a ^{2} + 3 a} 2 x

\frac{2 x}{3 x - 1} + \frac{- 4 x}{3 x - 1} \frac{2 x - 4 x}{3 x - 1} \frac{- 2 x}{3 x - 1}

x!= 1/3

\frac{3}{x + 1} + \frac{4}{x ^{2} - 3 x - 4} \frac{3}{x + 1} + \frac{4}{( x - 4 ) ( x + 1 )} \frac{3 ( x - 4 )}{( x + 1 ) ( x - 4 )} + \frac{4}{( x - 4 ) ( x + 1 )} \frac{3 ( x - 4 ) + 4}{( x + 1 ) ( x - 4 )} \frac{3 x - 8}{( x + 1 ) ( x - 4 )} x \neq = - 1, 4

\frac{2 t}{t - 4} - \frac{5 t}{t ^{2} - 16} \frac{2 t ( t + 4 )}{( t - 4 ) ( t + 4 )} - \frac{5 t}{( t - 4 ) ( t + 4 )} \frac{2 t ( t + 4 ) - 5 t}{( t - 4 ) ( t + 4 )} \frac{2 t ^{2} + 3 t}{( t - 4 ) ( t + 4 )} t \neq = 4, - 4

\frac{2 t + 1}{2 t ^{2} - 14 t + 24} + \frac{5 t}{4 t ^{2} - 8 t - 12} \frac{2 t + 1}{2 ( t ^{2} - 7 t + 12 )} + \frac{5 t}{4 ( t ^{2} - 2 t - 3 )} \frac{2 t + 1}{2 (( t - 4 ) ( t - 3 ))} + \frac{5 t}{4 (( t - 3 ) ( t + 1 ))} \frac{2 t + 1}{2 (( t - 4 ) ( t - 3 )) ( t + 1 )} + \frac{5 t}{4 (( t + 1 ) ( t - 3 ) ( t - 4 )} \frac{4 t + 2 ( t + 1 )}{4 (( t - 4 ) ( t - 3 )) ( t + 1 )} + \frac{5 t ( t - 4 )}{4 (( t + 1 ) ( t - 3 ) ( t - 4 )} \frac{4 t + 2 ( t + 1 ) + 5 t ( t - 4 )}{4 (( t - 4 ) ( t - 3 )) ( t + 1 )} \frac{( 4 t + 2 ) ( t + 1 ) + 5 t ( t - 4 )}{4 (( t - 4 ) ( t - 3 )) ( t + 1 )} \frac{4 t ^{2} + 6 t + 2 + 5 t ^{2} - 20 t}{4 (( t - 4 ) ( t - 3 )) ( t + 1 )} \frac{9 t ^{2} - 16 t + 2}{4 (( t - 4 ) ( t - 3 )) ( t + 1 )} t \neq = 4, 3, - 1

Maxim braxim :)

\frac{3}{4 x ^{2} + 7 x + 3} - \frac{5}{16 x ^{2} + 24 x + 9} \frac{3}{4 x ^{2} + 7 x + 3} - \frac{5}{4 x ( 4 x + 3 ) + 3 ( 4 x + 3 )} \frac{3 ( 4 x + 3 )}{( 4 x + 3 ) ( 4 x + 3 ) ( x + 1 )} - \frac{5 ( x + 1 )}{( 4 x + 3 ) ( 4 x + 3 ) ( x + 1 )} \frac{3 ( 4 x + 3 ) - 5 ( x + 1 )}{( 4 x + 3 ) ( 4 x + 3 ) ( x + 1 )} \frac{7 x + 4}{( 4 x + 3 ) ( 4 x + 3 ) ( x + 1 )} x \neq = - 3, - 1

y_{7} s \frac{3 m + 2}{2} + \frac{4 m + 5}{5} \frac{5 ( 3 m + 2 )}{10} + \frac{2 ( 4 m + 5 )}{10} \frac{15 m + 10}{10} + \frac{8 m + 10}{10} \frac{15 m + 10 + 8 m + 10}{10} \frac{23 m + 20}{10}

Simplify

\frac{7 a ^{2} b ^{3}}{2 1 ^{4} b} = \frac{a ^{2} b ^{2}}{3 a ^{4}} = \frac{b ^{2}}{3 a ^{2}}

(- x^{2} + 2 x + 7) + (2 x^{2} -7 x -7) = - x^{2} + 2 x + 7 + 2 x^{2} -7 x -7 = x^{2} -5 x

(2 m^{2} - mn + 4 n^{2}) - (5 m^{2} - mn + n^{2}) = 2 m^{2} - mn + 4 n^{2} - 5 m^{2} + mn - n^{2} = - 3 m^{2} + 3 n^{2} = 3 (- m^{2} + n^{2})

2 (12 a - 5) (3 a - 7) = (24 a - 10) (3 a - 7) = 72 a^{2} - 198 a + 70

b (n + 1) - b (n) = (2 (n + 1) + 1)^{3} - (2 n + 1)^{3} = (2 n + 3)^{3} - (2 n + 1)^{3} = (8 n^{3} + 36 n^{2} + 54 n + 27) - (8 n^{3} + 12 n^{2} + 6 n + 1) = 24 n^{2} + 48 n + 26

Factor
5.

x^{2} - 27 x + 72 = (x^{2} - 3 x) (- 24 x + 72) = x (x - 3) - 24 (x - 3) = (x - 24) (x - 3) -27 * 72 = -24,-3

\begin{align}
& (2x-y+1)^{2}-(x-y-2)^{2} \
&= [(2x - y + 1) + (x - y - 2)] [(2x - y + 1) - (x - y - 2)] \
&= [2x - y + 1 + x - y - 2] [2x - y + 1 - (-x + y + 2)] \
&= (3x - 2y - 1)(x + 3) \
\end{align}

simplify 5.$$ \begin{align} & \frac{8a-12}{10-10a} \\ &= \frac{4(2a-3)}{10(1-a)} \\ &= \frac{2(2a-3)}{5(1-a)} \end{align}

\frac{x ^{2} + 2 x - 3}{4 - 3 x - x ^{2}} = \frac{x ^{2} + 2 x - 3}{- ( x ^{2} + 3 x - 4 )} = \frac{( x + 3 ) ( x - 1 )}{- ( x + 4 ) ( x - 1 )} = \frac{x + 3}{- ( x + 4 )} = \frac{- ( x + 3 )}{x + 4}

add 3 prod -4

4 -1

Jason Cameron

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Maxim braxim :)

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