Question

How is (s-t)(s/t) equivalent to (s^2/t) -s

Answer 1

Explanation:

For the expression (s-t)(s/t) we first use the distributive property:

$(s-t)(\frac{s}{t}) \\ \\=s\times \frac{s}{t}-t\times \frac{s}{t}$

We can write both s and t as fractions by using a denominator of 1:

$\\=\frac{s}{1}\times \frac{s}{t}-\frac{t}{1}\times \frac{s}{t}$

To multiply frations, we multiply straight across:

$=\frac{s\times s}{1\times t}-\frac{t\times s}{1\times t} \\ \\=\frac{s^2}{t}-\frac{ts}{t}$

In the second fraction, st/t, the t will divide out, or cancel, since it is in both the numerator and denominator:

$\frac{s^2}{t}-s$

Answer 2

$(s-t)\cdot\dfrac{s}{t}=s\cdot\dfrac{s}{t}-t\cdot \dfrac{s}{t}=\dfrac{s^2}{t}-s$