What is the answer to (a-1)/(a+2)= a/(a-7) ?

The answer to (a-1)/(a+2)= a/(a-7) is a= 7/10

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(a-1)/(a+2)= a/(a-7)

\frac{a - 1}{a + 2} = \frac{a}{a - 7}

a = \frac{7}{10}

Decimal Notation

a = 0.7

Solution steps

\frac{a - 1}{a + 2} = \frac{a}{a - 7}

Cross multiply

a^{2} - 8 a + 7 = a^{2} + 2 a

Move

7

to the right side

a^{2} - 8 a = a^{2} + 2 a - 7

Subtract

a^{2} + 2 a

from both sides

a^{2} - 8 a - (a^{2} + 2 a) = a^{2} + 2 a - 7 - (a^{2} + 2 a)

Simplify

- 10 a = - 7

Divide both sides by

- 10

a = \frac{7}{10}

Verify Solutions

Find undefined (singularity) points:

a = - 2, a = 7

Combine undefined points with solutions:

a = \frac{7}{10}

x, y = \frac{2 x + 3}{5 x - 2}

\frac{2}{x + 1} = \frac{1}{x - 1}

\frac{48}{x} = 3

- \frac{12}{( x - 2 ) ^{2}} = - 3

\frac{x ^{2} + x - 6}{x - 2} = 0

What is the answer to (a-1)/(a+2)= a/(a-7) ?
The answer to (a-1)/(a+2)= a/(a-7) is a= 7/10
Solve for a: (a-1)/(a+2)= a/(a-7)
The solution is a= 7/10