adding and subtracting algebraic fractions - write as a single fraction in its simplest form
a) 3x/4 - x/8
b) 3x/4 - x/3
c)4/15x - 3/30x
+9466 a) \(\frac{3x}{4}-\frac{x}{8}\)
Multiply the first fraction by \(\frac22\)
\(=\,\frac22\cdot\frac{3x}{4}-\frac{x}{8}\\~\\ =\,\frac{6x}{8}-\frac{x}{8}\)
Now that we have a commond denominator we can combine the terms.
\(=\,\frac{6x-x}{8}\\~\\ =\,\frac{5x}{8}\)
b) \(\frac{3x}{4}-\frac{x}{3}\)
Multiply the first fraction by \(\frac33\) and the second fraction by \(\frac44\)
\(=\,\frac33\cdot\frac{3x}{4}-\frac{x}{3}\cdot\frac44\\~\\ =\,\frac{9x}{12}-\frac{4x}{12}\\~\\ =\,\frac{9x-4x}{12}\\~\\ =\,\frac{5x}{12}\)
c) Technically what you've written is \(\frac{4}{15}x-\frac{3}{30}x\) but I will do \(\frac{4}{15x}-\frac{3}{30x}\)
\(\frac{4}{15x}-\frac{3}{30x}\)
Multiply the first fraction by \(\frac22\)
\(=\,\frac22\cdot\frac{4}{15x}-\frac{3}{30x} \\~\\ =\,\frac{8}{30x}-\frac{3}{30x}\\~\\ =\,\frac{8-3}{30x}\\~\\ =\,\frac{5}{30x}\)
Now we can reduce this fraction by 5 .
\(=\,\frac{1}{6x}\)
+9466 a) \(\frac{3x}{4}-\frac{x}{8}\)
Multiply the first fraction by \(\frac22\)
\(=\,\frac22\cdot\frac{3x}{4}-\frac{x}{8}\\~\\ =\,\frac{6x}{8}-\frac{x}{8}\)
Now that we have a commond denominator we can combine the terms.
\(=\,\frac{6x-x}{8}\\~\\ =\,\frac{5x}{8}\)
b) \(\frac{3x}{4}-\frac{x}{3}\)
Multiply the first fraction by \(\frac33\) and the second fraction by \(\frac44\)
\(=\,\frac33\cdot\frac{3x}{4}-\frac{x}{3}\cdot\frac44\\~\\ =\,\frac{9x}{12}-\frac{4x}{12}\\~\\ =\,\frac{9x-4x}{12}\\~\\ =\,\frac{5x}{12}\)
c) Technically what you've written is \(\frac{4}{15}x-\frac{3}{30}x\) but I will do \(\frac{4}{15x}-\frac{3}{30x}\)
\(\frac{4}{15x}-\frac{3}{30x}\)
Multiply the first fraction by \(\frac22\)
\(=\,\frac22\cdot\frac{4}{15x}-\frac{3}{30x} \\~\\ =\,\frac{8}{30x}-\frac{3}{30x}\\~\\ =\,\frac{8-3}{30x}\\~\\ =\,\frac{5}{30x}\)
Now we can reduce this fraction by 5 .
\(=\,\frac{1}{6x}\)
