0
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Multiply either sides by LCM$(4,3)$ $\endgroup$ – lab bhattacharjee May 31 '14 at 6:15
  • $\begingroup$ @labbhattacharjee do I multiply everything on both sides by the LCM? $\endgroup$ – mahat May 31 '14 at 6:15
  • $\begingroup$ by doing that you should learn why LCM is used $\endgroup$ – lab bhattacharjee May 31 '14 at 6:17
  • $\begingroup$ Alternatively break $\frac{a+2}3$ to $\frac a3+\frac23$. $\endgroup$ – peterwhy May 31 '14 at 6:27
  • $\begingroup$ $$\frac {a}{4} = \frac{1} {4}a$$ $$\frac {a+2} {3} = \frac {1}{3}a + \frac {2} {3}$$ $\endgroup$ – Adola Jan 26 '17 at 5:17
0
$\begingroup$

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.

$a = -116$.

$\endgroup$
0
$\begingroup$

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.

$\endgroup$
0
$\begingroup$

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

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


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: $$-\frac {1} {12}a - \frac {2} {3} = 9$$ $$-\frac {1} {12}a = 9\frac {2} {3}$$ $$-\frac {1} {12}a = \frac {29} {3}$$ $$a = \frac {29} {3} * -\frac {12} {1}$$ $$a = \frac {29 * -12}{3 * 1}$$ $$a = \frac {-348} {3}$$ $$a = -116$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.