Question

7-b=b-87 ------------- 9 54 это дробное уравнение!!!! Пж решите!

Answer 1

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Answer 2

To solve the fractional equation $7-b = \frac{b}{87} - \frac{9}{54}$, we need to follow these steps:

Step 1: Find a common denominator for the fractions on the right side of the equation. The least common multiple (LCM) of 87 and 54 is 522, so we will convert both fractions to have a denominator of 522.

Step 2: Simplify and solve the equation for the variable $b$.

Let's proceed with the solution:

Step 1: Find a common denominator of 522:

$\frac{b}{87}$ can be rewritten as $\frac{b \cdot 6}{87 \cdot 6} = \frac{6b}{522}$

$\frac{9}{54}$ can be simplified as $\frac{9}{54} = \frac{1}{6}$

Now the equation becomes: $7 - b = \frac{6b}{522} - \frac{1}{6}$

Step 2: Simplify and solve the equation for $b$:

To get rid of the fractions, we can multiply the whole equation by the common denominator 522:

$522 \cdot (7 - b) = 522 \cdot \left(\frac{6b}{522} - \frac{1}{6}\right)$

Now we have:

$522 \cdot 7 - 522 \cdot b = 6b - 87$

Next, combine like terms:

$3654 - 522b = 6b - 87$

Move all terms with $b$ to one side of the equation:

$6b + 522b = 3654 - 87$

$528b = 3567$

Finally, solve for $b$:

$b = \frac{3567}{528}$

To simplify the fraction, you can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, $GCD(3567, 528) = 33$.

$b = \frac{3567}{528} = \frac{107}{16}$

So, the solution to the fractional equation is $b = \frac{107}{16}$.