How do I solve algebraic fractions with two fractions on one side?

How do I solve algebraic fractions with two fractions on one side?

$$\frac{a}{4}-\frac{a+2}{3}=9$$

Just like that one, what would I do? Please explain why you did what you did. I can't show working out for something I don't know how to do.

• Multiply either sides by LCM$(4,3)$ – lab bhattacharjee May 31 '14 at 6:15
• @labbhattacharjee do I multiply everything on both sides by the LCM? – mahat May 31 '14 at 6:15
• by doing that you should learn why LCM is used – lab bhattacharjee May 31 '14 at 6:17
• Alternatively break $\frac{a+2}3$ to $\frac a3+\frac23$. – peterwhy May 31 '14 at 6:27
• $$\frac {a}{4} = \frac{1} {4}a$$ $$\frac {a+2} {3} = \frac {1}{3}a + \frac {2} {3}$$ – Adola Jan 26 '17 at 5:17

Step 1: Find the common denominator: $3\cdot 4 = 12$

Step 2: Multiply both sides by common denominator $12$.

$12\cdot \left(\dfrac{a}{4} - \dfrac{a+2}{3}\right) = 12\cdot 9$.

Step 3: Distribute $12$ into the parentheses of the left side.

$12\cdot \dfrac{a}{4} - 12\cdot \dfrac{a+2}{3} = 108$, and simplify.

$3a - 4(a+2) = 108$, and simplify again.

$3a - 4a - 8 = 108$, and simplify again.

$-a - 8 = 108$, add $8$ both sides.

$-a - 8 + 8 = 108 + 8$, simplify.

$-a = 116$, and finally multiply $-1$ to both sides to get the answer.

$a = -116$.

Multiply the entire equation by all of the denominators, and then solve for A as if there were no fractions.

So in this case, multiply the entire equation by 4. Then multiply by 3.

$$\frac {a}{4} = \frac{1} {4}a$$ $$\frac {a+2} {3} = \frac {1}{3}a + \frac {2} {3}$$

$$\frac {1} {4}a-(\frac {1} {3}a + \frac {2} {3}) = 9$$ $$\frac{1}{4}a - \frac {1} {3}a - \frac {2}{3} = 9$$

Let's find the value of $\frac {1}{4}a -\frac {1}{3}a$. Then we will subtract the results by $\frac {2} {3}$ or add $-\frac {2}{3}$ $$\frac {1} {4}a -\frac{1}{3}a = \frac {3 - 4}{12}a = -\frac {1} {12}a$$ So: $$-\frac {1} {12}a - \frac {2} {3} = 9$$ $$-\frac {1} {12}a = 9\frac {2} {3}$$ $$-\frac {1} {12}a = \frac {29} {3}$$ $$a = \frac {29} {3} * -\frac {12} {1}$$ $$a = \frac {29 * -12}{3 * 1}$$ $$a = \frac {-348} {3}$$ $$a = -116$$