# How do you solve #a+1/2 + 3/2 = 1/a #?

You multiply everything by the same amount. But there is a shortcut in this particular case.

By signing up, you agree to our Terms of Service and Privacy Policy

To solve the equation a + 1/2 + 3/2 = 1/a, we can start by combining the fractions on the left side of the equation. This gives us (a + 1/2 + 3/2) = (2a + 1)/2.

Next, we can simplify the equation by finding a common denominator for the fractions on the left side. The common denominator is 2, so we have (2a + 1)/2 = 1/a.

To eliminate the fractions, we can multiply both sides of the equation by 2a. This gives us (2a + 1) = 2/a.

Expanding the equation, we have 2a + 1 = 2/a.

To get rid of the fraction, we can multiply both sides of the equation by a. This gives us a(2a + 1) = 2.

Expanding the equation again, we have 2a^2 + a = 2.

Rearranging the equation, we have 2a^2 + a - 2 = 0.

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring.

Factoring the quadratic equation, we have (2a - 1)(a + 2) = 0.

Setting each factor equal to zero, we have 2a - 1 = 0 or a + 2 = 0.

Solving these equations, we find that a = 1/2 or a = -2.

Therefore, the solutions to the equation a + 1/2 + 3/2 = 1/a are a = 1/2 and a = -2.

By signing up, you agree to our Terms of Service and Privacy Policy

- What are the important parts of the equation to graph #f(x) = (x^2 - 1) / (x+1)#?
- How do you simplify #[2x(x+6)^4-x^2(4)(x+6)^3]/(x+6)^8#?
- How do you simplify and find the excluded value of # (r + 6) / (r^2 - r - 6)#?
- How do you simplify #(x+3) /( x+1) div (x^2+5x+6)#?
- How do you simplify #(x+1)/3 = (2x-1)/4#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7