# Thread: Solving equations with rational terms.

1. ## Solving equations with rational terms.

Bit of help please on this fine Sunday morning

$\frac{x}{3}=\frac{2}{x}$

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

Rationals never where my strong point

Thank you!

Bit of help please on this fine Sunday morning

$\frac{x}{3}=\frac{2}{x}$ Mr F says: Cross multiply: ${\color{red}x^2 = 6}$. Solve this.

$\frac{2}{x + 1}=\frac{2x}{2x - 3} + 3$ Mr F says: Multiply both sides by (x + 1)(2x - 3):

${\color{red}2(2x - 3) = 2x(x+1) + 3(x + 1)(2x - 3)}$. Expand. Simplify. Solve.

Rationals never where my strong point

Thank you!
..

3. x = 2.449489743 x = 2

and

x=1

?

x = 2.449489743 x = 2

and

x=1

?
How are you getting three solutions to a quadratic equation?

5. Simplifying
x2 = 6

Solving
x2 = 6

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 6

Take the square root of each side:

x = {2.449489743}
__________________________________________________ _________________

Simplifying
2(2x + -3) = 2x(x + 1) + 3(x + 1)(2x + -3)

Reorder the terms:
2(-3 + 2x) = 2x(x + 1) + 3(x + 1)(2x + -3)
(-3 * 2 + 2x * 2) = 2x(x + 1) + 3(x + 1)(2x + -3)
(-6 + 4x) = 2x(x + 1) + 3(x + 1)(2x + -3)

Reorder the terms:
-6 + 4x = 2x(1 + x) + 3(x + 1)(2x + -3)
-6 + 4x = (1 * 2x + x * 2x) + 3(x + 1)(2x + -3)
-6 + 4x = (2x + 2x2) + 3(x + 1)(2x + -3)

Reorder the terms:
-6 + 4x = 2x + 2x2 + 3(1 + x)(2x + -3)

Reorder the terms:
-6 + 4x = 2x + 2x2 + 3(1 + x)(-3 + 2x)

Multiply (1 + x) * (-3 + 2x)
-6 + 4x = 2x + 2x2 + 3(1(-3 + 2x) + x(-3 + 2x))
-6 + 4x = 2x + 2x2 + 3((-3 * 1 + 2x * 1) + x(-3 + 2x))
-6 + 4x = 2x + 2x2 + 3((-3 + 2x) + x(-3 + 2x))
-6 + 4x = 2x + 2x2 + 3(-3 + 2x + (-3 * x + 2x * x))
-6 + 4x = 2x + 2x2 + 3(-3 + 2x + (-3x + 2x2))

Combine like terms: 2x + -3x = -1x
-6 + 4x = 2x + 2x2 + 3(-3 + -1x + 2x2)
-6 + 4x = 2x + 2x2 + (-3 * 3 + -1x * 3 + 2x2 * 3)
-6 + 4x = 2x + 2x2 + (-9 + -3x + 6x2)

Reorder the terms:
-6 + 4x = -9 + 2x + -3x + 2x2 + 6x2

Combine like terms: 2x + -3x = -1x
-6 + 4x = -9 + -1x + 2x2 + 6x2

Combine like terms: 2x2 + 6x2 = 8x2
-6 + 4x = -9 + -1x + 8x2

Solving
-6 + 4x = -9 + -1x + 8x2

Reorder the terms:
-6 + 9 + 4x + x + -8x2 = -9 + -1x + 8x2 + 9 + x + -8x2

Combine like terms: -6 + 9 = 3
3 + 4x + x + -8x2 = -9 + -1x + 8x2 + 9 + x + -8x2

Combine like terms: 4x + x = 5x
3 + 5x + -8x2 = -9 + -1x + 8x2 + 9 + x + -8x2

Reorder the terms:
3 + 5x + -8x2 = -9 + 9 + -1x + x + 8x2 + -8x2

Combine like terms: -9 + 9 = 0
3 + 5x + -8x2 = 0 + -1x + x + 8x2 + -8x2
3 + 5x + -8x2 = -1x + x + 8x2 + -8x2

Combine like terms: -1x + x = 0
3 + 5x + -8x2 = 0 + 8x2 + -8x2
3 + 5x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
3 + 5x + -8x2 = 0

Factor a trinomial.
(1 + -1x)(3 + 8x) = 0

the factor '(1 + -1x)'

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

the factor '(3 + 8x)'

Simplifying
3 + 8x = 0

Solving
3 + 8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8x = 0 + -3
8x = 0 + -3

Combine like terms: 0 + -3 = -3
8x = -3

Divide each side by '8'.
x = -0.375

Simplifying
x = -0.375

x = {1, -0.375}

6. Do my workings out figure out ok, i've been looking at it all afternoon but confused,

It looks like you've correctly smplified the equation to $8x^2 - 5x - 3= 0$. Your two solutions are correct, although I prefer to use fractions ...... -3/8 rather than -0.375.