Solve 10/h + 5 = 7/2 + h

Question

Solve the equation

h_{1} = - \frac{5}{2}, h_{2} = 4

Alternative Form

h_{1} = - 2.5, h_{2} = 4

Evaluate

\frac{10}{h} + 5 = \frac{7}{2} + h

Find the domain

\frac{10}{h} + 5 = \frac{7}{2} + h, h \neq = 0

Multiply both sides of the equation by LCD

(\frac{10}{h} + 5) \times 2 h = (\frac{7}{2} + h) \times 2 h

Simplify the equation

More Steps

20 + 10 h = (\frac{7}{2} + h) \times 2 h

Simplify the equation

More Steps

20 + 10 h = 7 h + 2 h^{2}

Move the expression to the left side

20 + 10 h - (7 h + 2 h^{2}) = 0

Calculate the sum or difference

More Steps

20 + 3 h - 2 h^{2} = 0

Factor the expression

More Steps

(4 - h) (5 + 2 h) = 0

When the product of factors equals 0,at least one factor is 0

4 - h = 0 5 + 2 h = 0

Solve the equation for h

More Steps

h = 4 5 + 2 h = 0

Solve the equation for h

More Steps

h = 4 h = - \frac{5}{2}

Check if the solution is in the defined range

h = 4 h = - \frac{5}{2}, h \neq = 0

Find the intersection of the solution and the defined range

h = 4 h = - \frac{5}{2}

Solution

h_{1} = - \frac{5}{2}, h_{2} = 4

Alternative Form

h_{1} = - 2.5, h_{2} = 4

Show Solution