1/x +1/x+16=1/15

Can someone help me with this problem

multiply each term by 15x

15 + 15 + 240x = x
239x = -30
x = -30/239

That is the correct solution for the way you presented the equation, but ....

I have a sneaking suspicion that you meant

1/x + 1/(x+16) = 1/15

In that case multiply each term by 15x(x+16)
You will end up with a quadratic

thanks Reiny for your help

Of course! I can help you with that problem. The equation you've provided is:

1/x + 1/(x + 16) = 1/15.

To solve this equation, we need to find the value(s) of x that make the equation true. Let's start by finding a common denominator for the fractions on the left side of the equation. The common denominator in this case is 15x(x + 16).

Multiplying each term by the common denominator, we get:

(15x(x + 16))(1/x) + (15x(x + 16))(1/(x + 16)) = (15x(x + 16))(1/15).

After simplifying, we have:

15(x + 16) + 15x = x(x + 16).

Now let's simplify the equation:

15x + 240 + 15x = x^2 + 16x.

Combining like terms:

30x + 240 = x^2 + 16x.

Rearranging the equation to make it quadratic:

x^2 + 16x - 30x - 240 = 0.

Simplifying further:

x^2 - 14x - 240 = 0.

Now we have a quadratic equation. To solve it, we can either factor it or use the quadratic formula. Factoring might require a bit of trial and error, so let's use the quadratic formula:

x = [-(-14) ± √((-14)^2 - 4(1)(-240))] / (2(1)).

Simplifying:

x = [14 ± √(196 + 960)] / 2.

x = [14 ± √1156] / 2.

x = [14 ± 34] / 2.

There are two possible solutions:

1. x = (14 + 34) / 2 = 48 / 2 = 24.
2. x = (14 - 34) / 2 = -20 / 2 = -10.

Therefore, the equation 1/x + 1/(x + 16) = 1/15 has two solutions: x = 24 and x = -10.