Operations with rational algebraic expressions


(1) Perform the multiplication of fractions:

\( \frac{a^2 b}{6c} \cdot \frac{25c^2}{2a^2 b^2} \)

\( \frac{(5a + 1c)^2}{2(3a - b)} \cdot \frac{4((2a)^2 - b^2)}{13a^2 - (2c)^2} \)

\( \left(\frac{ab}{3b + 1c}\right)^2 \cdot \frac{4c(2b + c)}{a^2 b^2} \)

(2) Perform the division of fractions:

\( \frac{18ab(c + d)}{6d^2} : \frac{39b(c + d)}{3ad} \)

\( \frac{14a + 6b}{bc^2 + c^3} : \frac{25a^2 - 24b^2}{c(b + c)} \)

\( \frac{16a^2 - y^2}{2a} : \frac{1a - y}{a + y} \)

(3) Calculate the value of the expression:

\( \frac{(2x - 6)^2}{x^2 - (10)^2} \cdot \frac{6x - 9}{x^2 + 6x} \cdot \frac{8x - 8}{x^2 + 6x} \)

za x = 7

\( \frac{(x - 11)^2}{x^2 - (14)^2} \cdot \frac{2x + 2}{x^2} \cdot \frac{6x + 6}{x^2 + 10x} \)

,
za x = 2 i 5

(4) Calculate the value of the expression:

\( \frac{39x^5 y^7}{z^{6} t^{3}} \cdot \frac{y^{3} z^{6}}{15x^2 t^{9}} \cdot \frac{29x^2 y}{zt} \), za \( x = 8 \)

\( \frac{26x^4 t^2}{z^{6} y^{10}} \cdot \frac{19y^3}{12x^2 t^{6}} \cdot \frac{22x^2 y^2}{z^{4} t^2} \), za \( z = 3 \)

(5) Perform the calculation:

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

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

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

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

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

: \( (12a^2 + 12a + 8) \)

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