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 |
|
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:
\( \frac{(x + 4)^2}{3x - 4} \) : |
\( (x^2 + 6x + 2) \) |
\( \frac{(4a + 1)^2}{3a - 2} \) |
: \( (12a^2 + 12a + 8) \) |
Share exercise: