Question

x+3
$\frac{x + 3}{2} - \frac{2x + 5}{3} = 1$
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Answer 1

Step-by-step explanation:

Whenever we have fractions in equations, we always want to get rid of them and get them to the other side if we can do.

The first thing you need to realise is that all of the denominators in the fractions have (x−5) as a factor.

Using this:

xx−5+32(x−5)−1−x6(x−5)+7−3(x−5)=1

We want to find the lowest common multiple of the coefficents of (x−5) , which are 1 , 2 , 6 , −3

It is quite obvious to know that 6 is the smallest number that each of the terms go into by integer amounts.

This being said, we can multiply each fraction by its corresponding factor of six, over itself. E.g, for 1 we multiply by 66 and for 2 , we multiply by 33 and so on.

After doing this to each of the terms, we get:

6x6(x−5)+96(x−5)−(1−x)6(x−5)+−146(x−5)=1

Now that we have like terms for the denominators, we can combine it all into one singular fraction:

6x+9−(1−x)−146(x−5)=1

To get rid of the bracket we have to flip each sign:

6x+9−1+x−146(x−5)=1

Now we can collect like terms:

7x−66(x−5)=1

Next, we multiply out the denominator:

7x−6=6(x−5)

Now we can expand our bracket again:

7x−6=6x−30

Next we get the x terms on the left:

x−6=−30

Finally, we get the constant terms on the right:

x=−24

There we have it, a full, step-by-step method if how to get derive x from the equation xx−5+32x−10−1−x6x−30+715−3x=1

To verify that our value for x is the correct solution, let’s plug it back into the equation:

−24−29+3−48−10−1+24−144−30+715+72=1

−24−29+3−58−25174+789=1

−144−174+9−174−25−174+−14−174=1

−144+9−25−14−174=1

−174−174=1