Simplify the expression.
Start Fraction 3 x plus 5 over 2 left parenthesis Start Fraction x plus 1 over 4 x End Fraction right parenthesis minus 1 End Fraction
(1 point)
Responses
Start Fraction 12 x plus 10 over 3 x plus 1 End Fraction
Image with alt text: Start Fraction 12 x plus 10 over 3 x plus 1 End Fraction
2x + 10
2 x + 10
Start Fraction 6 x squared plus 10 x over negative x plus 1 End Fraction
Image with alt text: Start Fraction 6 x squared plus 10 x over negative x plus 1 End Fraction
Start Fraction 12 x squared plus 10 x over 3 x plus 1 End Fraction
To simplify the expression, we need to first simplify each term individually and then combine them.
The first term: Start Fraction 3 x plus 5 over 2 left parenthesis Start Fraction x plus 1 over 4 x End Fraction right parenthesis
To simplify this, we need to first simplify the fraction inside the parenthesis:
Start Fraction x plus 1 over 4 x End Fraction
This can be simplified by multiplying the numerator and denominator by 4x:
Start Fraction 4x(x + 1) over 4x(4x) End Fraction
Simplifying further:
Start Fraction 4x^2 + 4x over 16x^2 End Fraction
Now, we can substitute this back into the original expression:
Start Fraction 3x + 5 over 2(4x^2 + 4x) End Fraction
The second term: minus 1
Now, we can simplify the expression by dividing each term by 2:
Start Fraction 3x + 5 over 8x^2 + 8x - 1
Therefore, the simplified expression is:
Start Fraction 3x + 5 over 8x^2 + 8x - 1
@bot
Simplify the following expression: start fraction 5 squared minus 4 over 5 plus 2 end fraction.
To simplify the given expression, we follow the order of operations (PEMDAS) and perform the calculations step by step.
Start by evaluating the exponent of 5 squared:
Start Fraction 5 squared minus 4 over 5 plus 2 End Fraction = Start Fraction 25 minus 4 over 5 plus 2 End Fraction
Next, perform the subtraction:
Start Fraction 25 minus 4 over 5 plus 2 End Fraction = Start Fraction 21 over 5 plus 2 End Fraction
Now, we need to find a common denominator for 5 and 2 to add the fractions together. The common denominator is 5, so we rewrite 2 as a fraction with 5 as the denominator:
Start Fraction 21 over 5 plus 2 over 1 End Fraction
Now that both fractions have a common denominator, we can combine them:
Start Fraction 21 over 5 plus 2 over 1 End Fraction = Start Fraction 21 plus 2 over 5 End Fraction
Finally, perform the addition:
Start Fraction 21 plus 2 over 5 End Fraction = Start Fraction 23 over 5 End Fraction
Therefore, the simplified expression is: Start Fraction 23 over 5 End Fraction.
To simplify the expression, we can follow these steps:
1. Distribute the numerator of the first fraction: 3x + 5, over the second fraction: (x + 1)/(4x).
This gives us (3x + 5) / (2[(x + 1)/(4x)]) - 1.
2. Simplify the second fraction: (x + 1)/(4x). Combine like terms in the numerator: x + 1.
3. Divide the first fraction by the second fraction by multiplying by the reciprocal of the second fraction.
This gives us (3x + 5) * (4x/(2(x + 1))) - 1.
4. Simplify the expression within the parentheses.
Multiplying 4x and 2 gives us 8x in the denominator and (3x + 5)/(x + 1) in the numerator.
So, we have (8x(3x + 5))/(x + 1) - 1.
5. Distribute the 8x: 24x^2 + 40x over (x + 1) - 1.
Therefore, the simplified expression is (24x^2 + 40x) / (x + 1) - 1.