13.07 Algebraic fractions with factorisation (Extended)
Factorise and simplify the following algebraic fractions:
\dfrac{6 x - 16}{12}
\dfrac{x - 4}{4 - x}
\dfrac{6 \left(p - q\right)^{2}}{6 p^{2} - 6 q^{2}}
\dfrac{2 x^{2} + 10 x - 100}{2 x + 20}
\dfrac{2 x + 10 y}{x + 5 y}
\dfrac{x-1}{x^{2} - 2 x + 1}
\dfrac{2 r - 8}{r^{2} - 16}
\dfrac{x^{2} + 14 x + 49}{x^{2} + 4 x - 21}
\dfrac{4 x^{2} + 7 x - 2}{6 + x - x^{2}}
\dfrac{x^{2} + x y + x z + y z}{x^{2} + 2 x y + y^{2}}
\dfrac{5 \left(k^{2} - 5\right)^{4} + 20 k \left(k^{2} - 5\right)^{5}}{15 \left(k^{2} - 5\right)^{4}}
Simplify:
\dfrac{27 - 27 x}{28} \times \dfrac{4}{9 x - 9}
\dfrac{5 x + 8}{8 x y^{2}} \times \dfrac{9 x y}{25 x + 40}
\dfrac{p + 7}{5} \times \dfrac{5 p - 2}{p^{2} + 14 p + 49}
\dfrac{9 x y + 18 x}{x - 9} \times \dfrac{x y - 3 x - 9 y + 27}{4 y^{2} + 8 y}
Factorise and simplify the following expressions:
\dfrac{k - 2}{5} \div \dfrac{4 k - 8}{15}
\dfrac{k - 1}{2} \div \dfrac{k^{2} - 1}{6}
\dfrac{3 m^{2} + 3 m}{7 m y z} \div \dfrac{10 m + 10}{3 m z}
\dfrac{\left(m + 5\right) \left(m + 6\right)}{25 \left(m + 8\right)} \div \dfrac{\left(m + 6\right) \left(m + 8\right)}{10 \left(m + 8\right)}
\dfrac{p^{2} + 5 q + p q + 5 p}{9 q p^{2} + 45 q} \times \dfrac{9 p^{2} + 45}{p^{2} + 14 p + 45}
\dfrac{5 x^{2} + 22 x + 8}{x^{2} - 16} \div \dfrac{25 x^{2} - 4}{20 x^{2} - 8 x}
\dfrac{6 p + 48}{p^{2} - 64} \div \dfrac{12 + 12 p}{p^{2} - 2 p - 48}
What expression is missing from the equation below?
\dfrac{4 k^{2} - 13 k - 12}{k^{2} - 2 k - 8} \times ⬚ \times \dfrac{1}{\left( 4 k + 3\right)} = 1
Simplify the following expressions:
\dfrac{3 x y}{12 y} \times \dfrac{4 y^{2}}{3 w x} \div \dfrac{15 w x}{3 w^{2}}
\left(\dfrac{q}{5} + \dfrac{q}{10}\right) \times \left(\dfrac{q}{5} - \dfrac{q}{10}\right)
\dfrac{x + 3}{x + 4} \div \dfrac{x + 3}{3} - \dfrac{1}{x + 4}
\left(\dfrac{2}{x + 1} - \dfrac{4}{\left(x + 1\right)^{2}}\right) \div \dfrac{x + 5}{\left(x + 1\right)^{2}}