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Answer:
To solve the equation \( \frac{5}{8}+\frac{4+x}{x+10}=0 \), we will need to find the value of x that makes the equation true.
First, let's simplify the equation by finding a common denominator for the fractions on the left side:
\( \frac{5}{8} + \frac{4+x}{x+10} = \frac{5(x+10)}{8(x+10)} + \frac{4+x}{x+10} \)
Combining the fractions, we have:
\( \frac{5(x+10) + (4+x)}{8(x+10)} = 0 \)
Multiplying both sides by the common denominator, we eliminate the denominators:
\( 5(x+10) + (4+x) = 0 \times 8(x+10) \)
Simplifying further:
\( 5x + 50 + 4 + x = 0 \)
Combining like terms:
\( 6x + 54 = 0 \)
Now, let's isolate the variable x:
\( 6x = -54 \)
Dividing both sides by 6:
\( x = -9 \)
Therefore, the value of x that satisfies the equation is -9.