Answer:
[tex]\frac{1}{3}[/tex]x-1
Step-by-step explanation:
([tex]\frac{5}{6}[/tex]x-7)-([tex]\frac{1}{2}[/tex]x-6) =
The - sign before 6 is turned into a + sign when the bracket is removed because the arithmetic operation before the bracket is - and two - makes the second - turn into a + (It's a rule I can't rlly explain it well but yea)
[tex]\frac{5}{6}[/tex]x-7-[tex]\frac{1}{2}[/tex]x+6 = [tex]\frac{5}{6}[/tex]x-1-[tex]\frac{1}{2}[/tex]x
-7+6 makes it a -1.
[tex]\frac{5}{6}[/tex]x-[tex]\frac{1}{2}[/tex]x-1 = [tex]\frac{5}{6}[/tex]x-[tex]\frac{3}{6}[/tex]x-1
To make the denominator of the two fractions the same, I multiplied the second fraction by 3 so that both denominators are 6.
[tex]\frac{5}{6}[/tex]x-[tex]\frac{3}{6}[/tex]x-1 = [tex]\frac{2}{6}[/tex]x-1
After making the denominator the same, I can directly do the equation for the numerators (5-3=2) and keep the denominator the same.
[tex]\frac{2}{6}[/tex]x-1 = [tex]\frac{1}{3}[/tex]x-1
Since 2/6 has a common factor which is 2, I can divide both the numerators and denominators so that the fraction can be simplified further into 1/3, its simplest form.
