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 |
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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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