How do you use cross multiplication to solve #\frac{2}{x+3}-\frac{1}{x+4}=0#?

Question

Abigail Allen · Accepted Answer

#2/{x+3}-1/{x+4}=0#

by adding #1/{x+4}#,

#=> 2/{x+3}=1/{x+4}#

by cross multiplication,

#=> 2cdot(x+4)=1cdot(x+3)#

by multiplying out,

#=> 2x+8=x+3#

by subtracting #x#,

#=>x+8=3#

by subtracting #8#,

#=> x=-5#

I hope that this was helpful.

Julia Adams · Answer

undefined To solve the equation \frac{2}{x+3}-\frac{1}{x+4}=0 using cross multiplication, we can follow these steps:

1. Multiply both sides of the equation by the common denominator, which is (x+3)(x+4).

2. Distribute the denominator to each term in the equation.

3. Simplify the equation by combining like terms.

4. Solve for x by isolating the variable on one side of the equation.

The detailed solution is as follows:

Step 1: Multiply both sides by (x+3)(x+4):
2(x+4) - (x+3)(x+4) = 0

Step 2: Distribute the denominator:
2x + 8 - (x^2 + 7x + 12) = 0

Step 3: Simplify the equation:
2x + 8 - x^2 - 7x - 12 = 0
-x^2 - 5x - 4 = 0

Step 4: Solve for x:
To solve this quadratic equation, we can either factor it or use the quadratic formula. Factoring is not possible in this case, so we'll use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -1, b = -5, and c = -4. Plugging these values into the quadratic formula:

x = (-(-5) ± √((-5)^2 - 4(-1)(-4))) / (2(-1))
x = (5 ± √(25 - 16)) / (-2)
x = (5 ± √9) / (-2)
x = (5 ± 3) / (-2)

This gives us two possible solutions:
x = (5 + 3) / (-2) = 8 / (-2) = -4
x = (5 - 3) / (-2) = 2 / (-2) = -1

Therefore, the solutions to the equation \frac{2}{x+3}-\frac{1}{x+4}=0 are x = -4 and x = -1.