Operations with rational algebraic expressions


(1) Perform the multiplication of fractions:

\( \frac{a^2 b}{6c} \cdot \frac{10c^2}{5a^2 b^2} \)

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

\( \left(\frac{ab}{5b + 1c}\right)^2 \cdot \frac{5c(2b + c)}{a^2 b^2} \)

(2) Perform the division of fractions:

\( \frac{14ab(c + d)}{6d^2} : \frac{25b(c + d)}{4ad} \)

\( \frac{11a + 2b}{bc^2 + c^3} : \frac{53a^2 - 40b^2}{c(b + c)} \)

\( \frac{8a^2 - y^2}{6a} : \frac{2a - y}{a + y} \)

(3) Calculate the value of the expression:

\( \frac{(4x - 2)^2}{x^2 - (8)^2} \cdot \frac{6x - 8}{x^2 + 2x} \cdot \frac{12x - 12}{x^2 + 3x} \)

za x = 7

\( \frac{(x - 11)^2}{x^2 - (13)^2} \cdot \frac{2x + 2}{x^2} \cdot \frac{6x + 4}{x^2 + 10x} \)

,
za x = 4 i 5

(4) Calculate the value of the expression:

\( \frac{39x^5 y^7}{z^{7} t^{2}} \cdot \frac{y^{3} z^{6}}{16x^2 t^{9}} \cdot \frac{29x^2 y}{zt} \), za \( x = 9 \)

\( \frac{40x^4 t^2}{z^{4} y^{10}} \cdot \frac{19y^3}{20x^2 t^{8}} \cdot \frac{28x^2 y^2}{z^{4} t^2} \), za \( z = 3 \)

(5) Perform the calculation:

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

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

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

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

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

: \( (6a^2 + 8a + 4) \)

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