Solve for b i=(5a)/(t+b)

$i = \frac{5 a}{t + b}$

Step 1

Rewrite the equation as $\frac{5 a}{t + b} = i$ .

$\frac{5 a}{t + b} = i$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$t + b, 1$

Remove parentheses.

$t + b, 1$

The LCM of one and any expression is the expression.

$t + b$

Step 3

Multiply each term in $\frac{5 a}{t + b} = i$ by $t + b$ to eliminate the fractions.

Multiply each term in $\frac{5 a}{t + b} = i$ by $t + b$ .

$\frac{5 a}{t + b} (t + b) = i (t + b)$

Simplify the left side.

Cancel the common factor of $t + b$ .

Cancel the common factor.

$\frac{5 a}{t + b} (t + b) = i (t + b)$

Rewrite the expression.

$5 a = i (t + b)$

Simplify the right side.

Apply the distributive property.

$5 a = i t + i b$

Step 4

Solve the equation.

Rewrite the equation as $i t + i b = 5 a$ .

$i t + i b = 5 a$

Subtract $i t$ from both sides of the equation.

$i b = 5 a - i t$

Divide each term in $i b = 5 a - i t$ by $i$ and simplify.

Divide each term in $i b = 5 a - i t$ by $i$ .

$\frac{i b}{i} = \frac{5 a}{i} + \frac{- i t}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i b}{i} = \frac{5 a}{i} + \frac{- i t}{i}$

Divide $b$ by $1$ .

$b = \frac{5 a}{i} + \frac{- i t}{i}$

Simplify the right side.

Simplify each term.

Multiply the numerator and denominator of $\frac{5 a}{i}$ by the conjugate of $i$ to make the denominator real.

$b = \frac{5 a}{i} \cdot \frac{i}{i} + \frac{- i t}{i}$

Multiply.

Combine.

$b = \frac{5 a i}{i i} + \frac{- i t}{i}$

Simplify the denominator.

Raise $i$ to the power of $1$ .

$b = \frac{5 a i}{i^{1} i} + \frac{- i t}{i}$

Raise $i$ to the power of $1$ .

$b = \frac{5 a i}{i^{1} i^{1}} + \frac{- i t}{i}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$b = \frac{5 a i}{i^{1 + 1}} + \frac{- i t}{i}$

Add $1$ and $1$ .

$b = \frac{5 a i}{i^{2}} + \frac{- i t}{i}$

Rewrite $i^{2}$ as $- 1$ .

$b = \frac{5 a i}{- 1} + \frac{- i t}{i}$

Move the negative one from the denominator of $\frac{5 a i}{- 1}$ .

$b = - 1 \cdot (5 a i) + \frac{- i t}{i}$

Rewrite $- 1 \cdot (5 a i)$ as $- (5 a i)$ .

$b = - (5 a i) + \frac{- i t}{i}$

Multiply $5$ by $- 1$ .

$b = - 5 (a i) + \frac{- i t}{i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$b = - 5 a i + \frac{- i t}{i}$

Divide $- 1 t$ by $1$ .

$b = - 5 a i - 1 t$

Rewrite $- 1 t$ as $- t$ .

$b = - 5 a i - t$

Solve for b i=(5a)/(t+b)

Related Questions

Support LCMGCF.com by disabling your adblocker.