What is the answer to 1/(7.5s+1)= a/(s+a) ?

The answer to 1/(7.5s+1)= a/(s+a) is s=0

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1/(7.5s+1)= a/(s+a)

\frac{1}{7.5 s + 1} = \frac{a}{s + a}

s = 0

Solution steps

\frac{1}{7.5 s + 1} = \frac{a}{s + a}

Cross multiply

s + a = 7.5 a s + a

Move

a

to the right side

s = 7.5 a s

Move

7.5 a s

to the left side

s - 7.5 a s = 0

Factor

s - 7.5 a s : s (1 - 7.5 a)

s (1 - 7.5 a) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

s = 0

Verify Solutions

Find undefined (singularity) points:

s = - \frac{2}{15}, s = - a

Combine undefined points with solutions:

s = 0

A^{2} + A^{- 1} = 0

b, a = \frac{2 a + 6 b}{3 b}

\frac{3 - 2}{9 b} = \frac{1}{3 b - 7}

\frac{2}{w} = \frac{7}{w + 5}

b, a = \frac{3 b - 1}{3 b - 4}

What is the answer to 1/(7.5s+1)= a/(s+a) ?
The answer to 1/(7.5s+1)= a/(s+a) is s=0