Rational Algebraic Expressions – Multiplication, Division, and Evaluation
(1) Perform the multiplication of fractions:
\( \frac{a^2 b}{4c} \cdot \frac{15c^2}{3a^2 b^2} \)
\( \frac{(5a + 1c)^2}{2(3a - b)} \cdot \frac{4((1a)^2 - b^2)}{13a^2 - (4c)^2} \)
\( \left(\frac{ab}{3b + 2c}\right)^2 \cdot \frac{3c(2b + c)}{a^2 b^2} \)
(2) Perform the division of fractions:
\( \frac{18ab(c + d)}{4d^2} : \frac{27b(c + d)}{4ad} \)
\( \frac{15a + 2b}{bc^2 + c^3} : \frac{69a^2 - 32b^2}{c(b + c)} \)
\( \frac{12a^2 - y^2}{2a} : \frac{3a - y}{a + y} \)
(3) Calculate the value of the expression:
\( \frac{(4x - 6)^2}{x^2 - (6)^2} \cdot \frac{6x - 9}{x^2 + 5x} \cdot \frac{10x - 10}{x^2 + 2x} \) | for \( x = 6 \) |
\( \frac{(x - 14)^2}{x^2 - (13)^2} \cdot \frac{3x + 2}{x^2} \cdot \frac{12x + 4}{x^2 + 15x} \) | for \( x = 4 \) and \( 7 \) |
(4) Calculate the value of the expression:
\( \frac{45x^5 y^7}{z^{6} t^{2}} \cdot \frac{y^{3} z^{6}}{17x^2 t^{9}} \cdot \frac{28x^2 y}{zt} \), for \( x = 9 \)
\( \frac{36x^4 t^2}{z^{6} y^{8}} \cdot \frac{15y^3}{14x^2 t^{7}} \cdot \frac{24x^2 y^2}{z^{5} t^2} \), for \( z = 3 \)
(5) Perform the calculation:
\( \frac{x^2 - 4xy + y^2}{xy + x^2} \cdot \frac{x^2 + 4xy + y^2}{x^2 - 1xy} \)
(6) Express the expression as a fraction:
\( \frac{(x + 1)^2}{4x - 3} \) : | \( (x^2 + 6x + 6) \) |
\( \frac{(4a + 3)^2}{3a - 1} \) | : \( (9a^2 + 16a + 8) \) |
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