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Ierofanga [76]
3 years ago
5

Write the pair of fractions as a pair of fractions with a common denominator

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
4 0

I'll do the first two problems to get you started

Problem 1

1/2 = 3/6

1/3 = 2/6

For the first fraction, I multiplied top and bottom by 3. Note how 3 is the denominator of the second fraction.

For the second fraction, I multiplied top and bottom by 2. Note how 2 is the denominator of the first fraction.

===============================================

Problem 2

1/2 = 5/10

3/5 = 6/10

Like with problem 1, I multiplied top and bottom of the first fraction by the value 5 which is the denominator of the second fraction. Likewise, I did the same for the second fraction using the first denominator. The steps are essentially the same, but the numbers are different.

Problem 3 will be handled the same way. I'll let you try it out.

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Step-by-step explanation:

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Solve the following equation by completing the square. 3x^2-3x-5=13
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we'll start off by grouping some

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\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2

so we know that the middle term in the trinomial, is really 2 times the other two without the exponent, well, in our case, the middle term is just "x", well is really -x, but we'll add the minus later, we only use the positive coefficient and variable, so we'll use "x" to find the last term.

\bf \stackrel{\textit{middle term}}{2(x)(?)}=\stackrel{\textit{middle term}}{x}\implies ?=\cfrac{x}{2x}\implies ?=\cfrac{1}{2}

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\bf \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2-\left[ \cfrac{1}{2} \right]^2 \right)=6\implies \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2 \right)-\left[ \cfrac{1}{2} \right]^2=6 \\\\\\ \left(x-\cfrac{1}{2} \right)^2=6+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{25}{4}\implies x-\cfrac{1}{2}=\sqrt{\cfrac{25}{4}} \\\\\\ x-\cfrac{1}{2}=\cfrac{\sqrt{25}}{\sqrt{4}}\implies x-\cfrac{1}{2}=\cfrac{5}{2}\implies x=\cfrac{5}{2}+\cfrac{1}{2}\implies x=\cfrac{6}{2}\implies \boxed{x=3}

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Step-by-step explanation:

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