still am not sure how to solve rational expression
x/[5(x+2)] + (x-3)/(x+2) = 7/5
Multiply both sides of the equation by (x+2) to get the x term out of the denominators. Then combine terms and use common denominators.
(x/5) + (x-3) = (7/5)(x+2) = (7/5)x + 7/10
(12/10)x - 28/10 = (14/10)x + 7/10
(2/10)x = -35/10
2x = -35
x = -17 1/2
To solve the rational expression
x/[5(x+2)] + (x-3)/(x+2) = 7/5,
follow these steps:
Step 1: Find a common denominator.
The denominators in this expression are 5(x+2) and (x+2). The least common denominator for these two terms is 5(x+2).
Step 2: Rewrite the expression using the common denominator.
Let's rewrite the expression:
x/[5(x+2)] + (x-3)/(x+2) = 7/5
= x/(5(x+2)) + 5(x-3)/(5(x+2)) = 7/5
Step 3: Combine the numerators over the common denominator.
The denominators are now the same, so combine the numerators:
[x + 5(x-3)] / (5(x+2)) = 7/5
[x + 5x - 15] / (5(x+2)) = 7/5
[6x - 15] / (5(x+2)) = 7/5
Step 4: Clear the fractions by multiplying both sides of the equation by the common denominator.
Multiply both sides of the equation by 5(x+2) to clear the fractions:
5(x+2) * [6x - 15] / (5(x+2)) = 7/5 * 5(x+2)
6x - 15 = 7(x+2)
Step 5: Expand and simplify the equation.
Distribute the factors:
6x - 15 = 7x + 14
Step 6: Solve for x.
Move all the terms containing x to one side and all the constants to the other side:
6x - 7x = 14 + 15
-x = 29
Step 7: Simplify the equation for x.
Divide both sides of the equation by -1:
x = -29
Therefore, the solution to the rational expression is x = -29.