Rational Algebraic Expressions – Multiplication, Division, and Evaluation
(1) Perform the multiplication of fractions:
\( \frac{a^2 b}{4c} \cdot \frac{10c^2}{4a^2 b^2} \)
\( \frac{(1a + 5c)^2}{6(3a - b)} \cdot \frac{4((3a)^2 - b^2)}{13a^2 - (4c)^2} \)
\( \left(\frac{ab}{24b + 21c}\right)^2 \cdot \frac{39c(2b + c)}{a^2 b^2} \)
(2) Perform the division of fractions:
\( \frac{20ab(c + d)}{19d^2} : \frac{35b(c + d)}{4ad} \)
\( \frac{26a + 2b}{bc^2 + c^3} : \frac{37a^2 - 43b^2}{c(b + c)} \)
\( \frac{19a^2 - y^2}{26a} : \frac{40a - y}{a + y} \)
(3) Calculate the value of the expression:
\( \frac{(3x - 5)^2}{x^2 - (13)^2} \cdot \frac{44x - 8}{x^2 + 4x} \cdot \frac{12x - 10}{x^2 + 5x} \) | for \( x = 5 \) |
\( \frac{(x - 12)^2}{x^2 - (14)^2} \cdot \frac{3x + 3}{x^2} \cdot \frac{12x + 4}{x^2 + 13x} \) | for \( x = 4 \) and \( 6 \) |
(4) Calculate the value of the expression:
\( \frac{45x^5 y^7}{z^{8} t^{3}} \cdot \frac{y^{3} z^{5}}{17x^2 t^{6}} \cdot \frac{29x^2 y}{zt} \), for \( x = 10 \)
\( \frac{26x^4 t^2}{z^{5} y^{10}} \cdot \frac{19y^3}{13x^2 t^{7}} \cdot \frac{28x^2 y^2}{z^{5} t^2} \), for \( z = 2 \)
(5) Perform the calculation:
\( \frac{x^2 - 3xy + y^2}{xy + x^2} \cdot \frac{x^2 + 3xy + y^2}{x^2 - 2xy} \)
(6) Express the expression as a fraction:
\( \frac{(x + 3)^2}{2x - 2} \) : | \( (x^2 + 8x + 4) \) |
\( \frac{(3a + 1)^2}{3a - 3} \) | : \( (12a^2 + 8a + 2) \) |