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3 years ago

If you have the following equation, 2/3x+5/6-x=2-3/4x what would you multiply each term by to get rid of all the fractions

Mathematics

1 answer:

Genrish500 [490]3 years ago

5 0

Answer:

The answer is 12.

Step-by-step explanation:

You would multiply each of them by 12 to get rid of all of the fractions.

This is because 12 is the least common multiple of the denominators. You can find that by lining up their multiples and looking for the one that is the smallest that they have in common.

3: 3, 6, 9. 12. 15

4: 4. 8. 12. 16, 20

6: 6. 12. 18. 24. 30

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Let t as y² + 5y .

${y}^{2} + 5y = t$

Rewrite the equation :

$t - \frac{36}{t} = 0 \\$

Multiply sides by t

$t \times (t - \frac{36}{t} ) = t \times 0 \\$

${t}^{2} - 36 = 0$

Add sides 36

${t}^{2} - 36 + 36 = 0 + 36$

${t}^{2} = 36$

$t = ± \: 6$

_________________________________

So :

${y}^{2} + 5y = 6$

Subtract sides 6

${y}^{2} + 5y - 6 = 6 - 6$

${y}^{2} + 5y - 6 = 0$

$(y + 6)(y - 1) = 0$

$y = - 6 \: \: or \: \: y = 1$

##############################

${y}^{2} +5y = - 6$

$No \: \: solution$

_________________________________

Thus (( y = 1 )) and (( y = - 6 )) are the roots of the equation .

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3 years ago

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using the rule of exponents

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Hope this helps!

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