Algebraic Fractions
- To simplify an algebraic fraction, we find the highest common factor (HCF) of the numerator and the denominator.
\(\(\frac{3y+3}{y^2+7y+6}\)\)
\(\(\frac{3(y+1)}{(y+1)(y+6)}\)\)
\(\(\frac{3}{y+6}\)\)
\(\(\frac{x^2-36}{x^2+7x+10}\div \frac{x-6}{x+2}\)\)
\(\(\frac{x^2-36}{x^2+7x+10}\times \frac{x+2}{x-6}\)\)
\(\(\frac{ (x-6)(x+6)}{(x+5)(x+2)}\times \frac{x+2}{x-6}\)\)
\(\(\frac{\cancel{ (x-6) }(x+6)}{(x+5)\cancel{ (x+2) }}\times \frac{\cancel{ x+2 }}{\cancel{ x-6 }}\)\)
\(\(\frac{x+6}{x+5}\)\)
\(\(\frac{4x-12}{x^2-4}\times \frac{x^2+2x}{x^2-2x-3}\)\)
\(\(\frac{4(x-3)}{(x+2)(x-2)}\times \frac{x(x+2)}{(x-3)(x+1)}\)\)
\(\(\frac{4\cancel{ (x-3) }}{\cancel{ (x+2) }(x-2)}\times \frac{x\cancel{ (x+2) }}{\cancel{ (x-3) }(x+1)}\)\)
\(\(\frac{4x}{(x-2)(x+1)}\)\)
\(\(\frac{2(y+4)+7y}{y(y+4)}\)\)
\(\(\frac{2y+8+7y}{y(y+4)}\)\)
\(\(\frac{9y+8}{y(y+4)}\)\)
\(\(\frac{2x(x+3)-(x-5)}{(x-5)(x+3)}\)\)
\(\(\frac{2x^2+6x-x-5}{(x-5)(x+3)}\)\)
\(\(\frac{2x^2+5x-5}{(x-5)(x+3)}\)\)
\(\(\frac{x^2-5x}{6x-30}\)\)
\(\(\frac{x\cancel{ (x-5) }}{6\cancel{ (x-5) }}\)\)
\(\(\frac{x}{6}\)\)