Operations with rational algebraic expressions


(1) Perform the multiplication of fractions:

\( \frac{a^2 b}{8c} \cdot \frac{20c^2}{4a^2 b^2} \)

\( \frac{(4a + 4c)^2}{5(3a - b)} \cdot \frac{3((2a)^2 - b^2)}{15a^2 - (1c)^2} \)

\( \left(\frac{ab}{5b + 3c}\right)^2 \cdot \frac{5c(2b + c)}{a^2 b^2} \)

(2) Perform the division of fractions:

\( \frac{16ab(c + d)}{2d^2} : \frac{26b(c + d)}{4ad} \)

\( \frac{6a + 2b}{bc^2 + c^3} : \frac{25a^2 - 48b^2}{c(b + c)} \)

\( \frac{12a^2 - y^2}{6a} : \frac{3a - y}{a + y} \)

(3) Calculate the value of the expression:

\( \frac{(4x - 4)^2}{x^2 - (10)^2} \cdot \frac{7x - 8}{x^2 + 5x} \cdot \frac{12x - 12}{x^2 + 5x} \)

za x = 7

\( \frac{(x - 13)^2}{x^2 - (14)^2} \cdot \frac{3x + 2}{x^2} \cdot \frac{9x + 2}{x^2 + 12x} \)

,
za x = 1 i 7

(4) Calculate the value of the expression:

\( \frac{30x^5 y^7}{z^{6} t^{2}} \cdot \frac{y^{3} z^{6}}{15x^2 t^{7}} \cdot \frac{25x^2 y}{zt} \), za \( x = 8 \)

\( \frac{34x^4 t^2}{z^{4} y^{8}} \cdot \frac{18y^3}{14x^2 t^{7}} \cdot \frac{30x^2 y^2}{z^{5} t^2} \), za \( z = 2 \)

(5) Perform the calculation:

\( \frac{x^2 - 4xy + y^2}{xy + x^2} \cdot \frac{x^2 + 3xy + y^2}{x^2 - 2xy} \)

(6) Represent the expression in the form of a fraction:

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

\( (x^2 + 4x + 6) \)

\( \frac{(2a + 3)^2}{3a - 1} \)

: \( (12a^2 + 16a + 4) \)

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