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vlada-n [284]
3 years ago
9

How can you tell if this equation is true. 1/2+3/8 =4/10=2/5

Mathematics
2 answers:
Alekssandra [29.7K]3 years ago
6 0

Answer:  You could check it by doing what i did....

* Hope this helps:) Mark me the brainliest:)))!!!

Tanya [424]3 years ago
5 0

Answer:

In a very simple way, it can be verified that the equation is correct by making the divisions that the fractions represent, and checking that the result of these divisions is the same, as presented by the equation.

That is, by making the division of 1/2 and adding it to the division of 3/8, the result of said sum should be equal to 4/10 and 2/5.

Therefore, I will perform this calculation to verify if the equation is correct:

1/2+3/8 =4/10=2/5

0.5 + 0.375 = 0.4

0.875 = 0.4

As we can see, the equation is absolutely false, since the sum of 1/2 + 3/8 does not result in 4/10 or 2/5 (which are the same fraction, but simplified) but 7/8 (7 / 8 = 0.875).

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The value of x is –7.

Solution:

Given expression:

$\left(\frac{1}{x+3}+\frac{6}{x^{2}+4 x+3}\right) \cdot \frac{x+3}{x+1}

Let us factor x^2+4x+3.

x^2+4x+3=(x+1)(x+3)

Substitute this in the fraction.

$\left(\frac{1}{x+3}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

To make the denominator same, multiply and divide the first term by (x +1).

$\left(\frac{(x+1)}{(x+1)(x+3)}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

Denominators are same, you can add the fractions.

$\left(\frac{x+1+6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

$\frac{x+7}{(x+1)(x+3)} \cdot \frac{x+3}{x+1}

Cancel the common term in the numerator and denominator.

$\frac{x+7}{x+1} \cdot \frac{1}{x+1}

Multiply the fractions.

$\frac{x+7}{(x+1)^2}

$\frac{x+7}{x^2+2x+1}

The expression is simplified to one rational expression.

Suppose the expression is equal to 0.

$\frac{x+7}{x^2+2x+1}=0

Do cross multiplication.

${x+7}=0\times (}{x^2+2x+1})

Any number or variable multiplied by 0 gives 0.

${x+7}=0

Subtract 7 from both sides of the equation.

${x+7-7}=0-7

x = –7

The value of x is –7.

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