Subtract the following and simplify the difference if possible. x + 5 4 x − 2 x − 1 4 x \frac{x+5}{4x}-\frac{2x-1}{4x}

So here we're asked to subtract the following and simplify the difference if possible. We have x plus five over four x minus two x minus one over four x. Now when adding or subtracting rational expressions, we need to take a look and see if we have a common denominator, which I can see that we do, we have 4x. So that means in the numerator we're going to have x plus five minus, and then we have 2x minus one, and then in the denominator we're going to have four x. Now from here what I need to do is simplify what we have in the numerator. Now what I can see is we do have a subtraction that's happening here, and a subtraction is basically just like having a negative one that gets distributed into this second term that we see. So what we're gonna have is x plus five, and we need to distribute a negative sign into each of these terms. That's gonna be minus two x, negative two x. And then a a negative times a negative gives us a positive, so that's going to be plus one, and then all of that's going to be over four x. Now from here, what I can do is combine things in the numerator. We have a five and a one. Five plus one is six. And then we have a negative two x and a positive x. Negative two x plus positive one x is going to give us negative one x. So it's gonna be negative x, right, plus six all over four x. And there's really not another way I can factor or simplify anything from here. What I am going to do is switch the order and actually have the x be the next term. So we're gonna have six, and it's gonna be minus x. Just so I can write this minus sign, and that's gonna be all over four x. And and that's going to be my simplified answer. Now what we had before was correct to negative x plus six over four x, But I went ahead and just switched these just so we could write it as a minus sign, just because I don't like having this negative sign out front. But that is how we can go about solving a problem like this. So hope you found this helpful, and I'll see you all in the next video.

8. Rational Expressions and Equations

Adding and Subtracting Rational Expressions with Common Denominators

Beginning & Intermediate Algebra

8. Rational Expressions and Equations

Adding and Subtracting Rational Expressions with Common Denominators

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Multiple Choice

Subtract the following and simplify the difference if possible.
$\frac{x + 5}{4 x} - \frac{2 x - 1}{4 x}$

$\frac{x - 6}{4 x}$

$\frac{6 - x}{4 x}$

$$\frac$54x$

$\frac{6}{4x}$

Verified step by step guidance

Identify that both fractions have the same denominator, which is \$4x$. This allows you to subtract the numerators directly while keeping the denominator the same.

Write the subtraction of the numerators as a single expression: $(x + 5) - (2x - 1)$.

Distribute the subtraction sign across the second numerator: $x + 5 - 2x + 1$.

Combine like terms in the numerator: $(x - 2x) + (5 + 1)$.

Write the simplified numerator over the common denominator \$4x$ to get the simplified difference.

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Subtract the following and simplify the difference if possible.x+54x−2x−14x\(\frac{x+5}{4x}\)-\(\frac{2x-1}{4x}\)

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Subtract the following and simplify the difference if possible.
$\frac{x + 5}{4 x} - \frac{2 x - 1}{4 x}$