First write the value that makes the denominator zero then solve the equation x-8/2x+5=x+6/x
Your School Subject is Math, not college.
To find the value that makes the denominator zero in the equation (x-8)/(2x+5) = (x+6)/x, we need to set the denominators, 2x+5 and x, equal to zero separately.
Setting 2x+5 = 0, we subtract 5 from both sides and solve for x:
2x = -5
Divide both sides by 2 to isolate x:
x = -5/2
Setting x = 0, we can see that the denominator x becomes zero as well. However, in this case, we already know that the solution x = -5/2 will render the denominator zero. So there is no need to solve further for this particular equation.
Once we have identified the values that make the denominators zero, we can proceed to solve the equation for all other x-values.
Now let's solve the equation (x-8)/(2x+5) = (x+6)/x:
Cross multiply to eliminate the denominators:
x(x-8) = (x+6)(2x+5)
Expand the equation:
x^2 - 8x = 2x^2 + 17x + 30
Rearrange the equation to make it equal to zero:
0 = 2x^2 + 17x + 30 - x^2 + 8x
Combine like terms:
0 = x^2 + 25x + 30
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's factor it by finding two numbers whose product is 30 and whose sum is 25:
Factors of 30:
1, 30
2, 15
3, 10
5, 6
Among these pairs, the pair that adds up to 25 is 5 and 6.
Rewrite the equation:
0 = (x + 5)(x + 6)
Set each factor equal to zero:
x + 5 = 0 or x + 6 = 0
Solve for x:
x = -5 or x = -6
Therefore, the solutions to the equation are:
x = -5/2, -5, -6