Title: 14. Algebraic fractions involving factorising
Course: Demonstrating STACK (v4.4.7)

Reduce the following fraction to it's lowest terms: \[ [value]. \]
Feedback: By factorisng the numerator we obtain: \[\frac[value][value]. \] Then we can simplify the constants from the numerator and denominator to obtain: \[ [value]. \]

Reduce the following fraction to it's lowest terms: \[ [value]. \]
Feedback: By factorisng the numerator and denominator we obtain: \[\frac[value][value]. \] Then we can simplify the constants from the numerator and denominator to obtain: \[ [value]. \]

Reduce the following fraction to it's lowest terms: \[ [value]. \]
Feedback: By factorisng the denominator we obtain: \[\frac[value][value]. \] Then we can cancel the \([value]\) from the numerator and denominator to obtain: \[ [value]. \]

Reduce the following fraction to it's lowest terms: \[ [value]. \]
Feedback: By factorisng the numerator and the denominator we obtain: \[\frac[value][value]. \] Then we can cancel the \([value]\) from the numerator and denominator to obtain: \[ [value]. \]

Reduce the following fraction to it's lowest terms: \[ [value]. \]
Feedback: By factorisng the numerator and the denominator we obtain: \[\frac[value][value]. \] Then we can cancel the \([value]\)'s and constants from the numerator and denominator to obtain: \[ [value]. \]

Cancel factors to reduce the following fraction to it's simplest terms: \[ [value]. \]
Feedback: By factorisng the numerator and the denominator we obtain: \[\frac[value][value].\] Then we can cancel the \([value]\)'s and constants from the numerator and denominator to obtain: \[ [value]. \]

Reduce the following fraction to it's lowest terms: \[ [value]. \]
Feedback: By factorisng the numerator and the denominator we obtain: \[\frac[value][value]. \] Then we can cancel the compound term, \([value]\) from the numerator and denominator to obtain: \[ [value]. \]

Reduce the following fraction to it's simplest terms: \[ [value]. \]
Feedback: By factorisng the numerator and the denominator we obtain: \[\frac[value][value]. \] Then we can cancel the compound term, \([value]\) from the numerator and denominator to obtain: \[ [value]. \]

Express the following as a single fraction: \[ [value]. \]
(Hint: Try factorising the fractions.)
Feedback: When adding or subtracting algebraic fractions, just using the general rule can create alot more work if the denominators of the fractions have common factors. In this example, if we factorise the denominators we obtain: \[ \frac[value][value]+\frac[value][value]. \] It is clear that the factor \([value]\) is common in both denominators and so there is no need for our common denominator to contain this factor twice. Therefore, we take the common denominator \([value]\): \[ \frac[value][value]+\frac[value][value] = [value]. \]

Express the following as a single fraction: \[ \frac[value][value]\cdot\frac[value][value]. \]
(Hint: Try factorising the fractions.)
Feedback: When multiplying fractions you can save work if the denominator of one fraction has common factors with the numerator of another. In this example, if we factorise the denominator of the first fraction we obtain: \[ \frac[value][value]\cdot\frac[value][value]. \] It is clear that the factor \([value]\) is common in both fractions and so we can cancel \([value]\): \[ \frac[value][value]\cdot\frac{1}[value] = [value]. \]

Express the following as a single fraction: \[ \frac[value][value]\div\frac[value][value]. \]
(Hint: Try factorising the fractions.)
Feedback: When dividing fractions you can save work if the denominator or numerator of one fraction has common factors with the denominator or numerator respectively. Factorising these fractions gives: \[ \frac[value][value]\div\frac[value][value]. \] It is clear that the factor \([value]\) is common in both fractions and so we can cancel \([value]\): \[ \frac[value][value]\div[value] = [value]. \]