Solve for x
5/x-2 + 2/x+5 = 4/x^2+3x-10
not sure i know how to do this
Do you mean 5/(x-2) plus 2/(x+5) =
4/(x^2 + 3x -10)
To do this you either need a common denominator or to clear denominators.
I have to check the factors of the denomonators.
(x^2 + 3x -10) factors to (x+5)(x-2)
5/(x-2) needs to be multiplied by (x+5)/(x+5)
2/(x+5) needs to be multiplied by (x+2)/(x+2)
Can you finish from here?
yes that is what i meant.
i think i am still confused cause when i do that i got (7x+29)/(2x^2+6x-20)
which i don't think is right
7x + 29 is correct in the numerator.
the denominator will be x^2 + 3x - 10
Your mistake is that you added the denominators. You have to keep the denominator and add the numerators when working with fractions. Like 1/5 + 2/5 = 3/5
this is the same denominator that you have on the other side of the equation.
We are saying two fractions are equal, since there denominators are equal, then their numerators must also be equal.
Set 7x +29 = 4 and solve for x.
for x i got -3.57 is this correct?
To solve for x in this equation, we need to find the value of x that satisfies the equation. Here's a step-by-step guide on how to solve it:
Step 1: Get rid of the denominators by multiplying each term by the least common denominator (LCD) of all the denominators (x - 2, x + 5, x^2 + 3x - 10). To find the LCD, factor the denominators and take the product of their unique factors:
x - 2 = (x - 2)
x + 5 = (x + 5)
x^2 + 3x - 10 = (x - 2)(x + 5)
Since (x - 2) appears in both denominators, (x - 2) is the LCD.
Multiply each term by (x - 2):
(x - 2) * (5 / (x - 2)) + (x - 2) * (2 / (x + 5)) = (x - 2) * (4 / ((x - 2)(x + 5)))
5 + 2(x - 2) = 4
Step 2: Simplify the equation:
5 + 2x - 4 = 4
2x + 1 = 4
Step 3: Move the constant term (1) to the right side of the equation by subtracting it from both sides:
2x + 1 - 1 = 4 - 1
2x = 3
Step 4: Solve for x by dividing both sides of the equation by 2:
(2x) / 2 = 3 / 2
x = 3 / 2
Therefore, the solution to the equation 5/x - 2 + 2/x + 5 = 4/x^2 + 3x - 10 is x = 3/2.