Solve 6/a -7=a- 49/(a^(2)-7a) 1/a

Question

Solve the equation

a_{1} \approx - 7.821193, a_{2} \approx 7.074035

Evaluate

\frac{6}{a} - 7 = a - \frac{49}{a ^{2} - 7 a} \times \frac{1}{a}

Find the domain

More Steps

\frac{6}{a} - 7 = a - \frac{49}{a ^{2} - 7 a} \times \frac{1}{a}, a \in (- \infty, 0) \cup (0, 7) \cup (7, + \infty)

Multiply the terms

More Steps

\frac{6}{a} - 7 = a - \frac{49}{a ( a ^{2} - 7 a )}

Multiply both sides of the equation by LCD

(\frac{6}{a} - 7) a (a^{2} - 7 a) = (a - \frac{49}{a ( a ^{2} - 7 a )}) a (a^{2} - 7 a)

Simplify the equation

More Steps

55 a^{2} - 42 a - 7 a^{3} = (a - \frac{49}{a ( a ^{2} - 7 a )}) a (a^{2} - 7 a)

Simplify the equation

More Steps

55 a^{2} - 42 a - 7 a^{3} = a^{4} - 7 a^{3} - 49

Cancel equal terms on both sides of the expression

55 a^{2} - 42 a = a^{4} - 49

Move the expression to the left side

55 a^{2} - 42 a - (a^{4} - 49) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

55 a^{2} - 42 a - a^{4} + 49 = 0

Calculate

a \approx - 7.821193 a \approx 7.074035

Check if the solution is in the defined range

a \approx - 7.821193 a \approx 7.074035, a \in (- \infty, 0) \cup (0, 7) \cup (7, + \infty)

Find the intersection of the solution and the defined range

a \approx - 7.821193 a \approx 7.074035

Solution

a_{1} \approx - 7.821193, a_{2} \approx 7.074035

Show Solution

Solve the equation

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