((9)/(5)×(4)/(3))+((6)/(5)×(4)/(3))+((4)/(5)×(1)/(3))+[((-2)/(5))×((4)/(3))]

Identify common factor: Identify the common factor in each term of the expression, which is (4)/(3), except for the third term which has (1)/(3). We can factor out (4)/(3) from the first, second, and fourth terms.Factor out common factor: Factor out (4)/(3) from the first, second, and fourth terms. ((9)/(5)×(4)/(3))+((6)/(5)×(4)/(3))+((4)/(5)×(1)/(3))+((-2)/(5)×(4)/(3)) = (4)/(3) × [(9)/(5) + (6)/(5) - (2)/(5)] + (4)/(5)×(1)/(3)Combine and simplify: Combine the terms inside the brackets and simplify the third term. [(9)/(5) + (6)/(5) - (2)/(5)] = (13)/(5) (4)/(5)×(1)/(3) = (4)/(15)Substitute simplified terms: Substitute the simplified terms back into the expression. = (4)/(3) × (13)/(5) + (4)/(15)Multiply fractions: Multiply (4)/(3) by (13)/(5). =(4×13)/(3×5) =(52)/(15)Add fractions: Add (52)/(15) and (4)/(15) together. =(52)/(15) + (4)/(15) =(56)/(15)Simplify final fraction: Simplify the fraction (56)/(15) if possible. =(56)/(15) cannot be simplified further as 56 and 15 have no common factors other than 1.

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((9)/(5)×(4)/(3))+((6)/(5)×(4)/(3))+((4)/(5)×(1)/(3))+[((-2)/(5))×((4)/(3))]

$\left(\frac{9}{5} \times \frac{4}{3}\right)+\left(\frac{6}{5} \times \frac{4}{3}\right)+\left(\frac{4}{5} \times \frac{1}{3}\right)+\left[\left(\frac{-2}{5}\right) \times\left(\frac{4}{3}\right)\right]$

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Precalculus

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\left(\frac{9}{5} \times \frac{4}{3}\right)+\left(\frac{6}{5} \times \frac{4}{3}\right)+\left(\frac{4}{5} \times \frac{1}{3}\right)+\left[\left(\frac{-2}{5}\right) \times\left(\frac{4}{3}\right)\right]

Identify common factor: Identify the common factor in each term of the expression, which is $(\frac{4}{3})$ , except for the third term which has $(\frac{1}{3})$ . We can factor out $(\frac{4}{3})$ from the first, second, and fourth terms.
Factor out common factor: Factor out $(4)/(3)$ from the first, second, and fourth terms. $((9)/(5)\times(4)/(3))+((6)/(5)\times(4)/(3))+((4)/(5)\times(1)/(3))+((-2)/(5)\times(4)/(3))$ = $(4)/(3) \times [(9)/(5) + (6)/(5) - (2)/(5)] + (4)/(5)\times(1)/(3)$
Combine and simplify: Combine the terms inside the brackets and simplify the third term. $\newline$ $(\frac{9}{5} + \frac{6}{5} - \frac{2}{5}) = \frac{13}{5}$ $\newline$ $(\frac{4}{5}\times\frac{1}{3}) = \frac{4}{15}$
Substitute simplified terms: Substitute the simplified terms back into the expression. $\newline$ $= \frac{4}{3} \times \frac{13}{5} + \frac{4}{15}$
Multiply fractions: Multiply $(\frac{4}{3})$ by $(\frac{13}{5})$ . $=(\frac{4\times13}{3\times5})$ $=(\frac{52}{15})$
Add fractions: Add $(\frac{52}{15})$ and $(\frac{4}{15})$ together. $\newline$ $=(\frac{52}{15}) + (\frac{4}{15})$ $\newline$ $=(\frac{56}{15})$
Simplify final fraction: Simplify the fraction $(56)/(15)$ if possible. $=(56)/(15)$ cannot be simplified further as $56$ and $15$ have no common factors other than $1$ .