WASHINGTON -- As she wrapped up her remarks about the stunning, late-night sniper killing of five police officers and shooting of seven others, America's top law-enforcement officer sought to conclude on an optimistic note Friday.

"We are one nation, we are one people, and we stand together," said Attorney-General Loretta Lynch.

That hopeful proposition is under violent strain.

Two of the most potent sources of strife in this country have just collided: race and guns. In a week of police killing two black men; protests in multiple cities; finger-pointing over gun laws; and a shooter firing at officers in Dallas, the truths of a divided nation appeared to be self-evident.

Canada's prime minister expressed sorrow over the various tragedies: "Canadians are shocked by the cowardly attacks against police in Dallas. Our solidarity is with all victims of violence on this tragic week," Justin Trudeau tweeted.

People scrutinized the more selective offering of condolences from the U.S. firearms lobby. The National Rifle Association expressed sorrow over the fallen officers in Dallas, but not for the school-cafeteria worker in Minnesota.

Philando Castile had been pulled over for a busted tail light. According to his girlfriend, he informed police he was legally carrying a weapon, and was shot as he reached for his license. As he bled to death, a police officer screamed at them, she was separated from her four-year-old daughter, and arrested.

Protests formed in several cities -- including Dallas.

That's where police say Afghanistan veteran Micah Johnson established a vantage point from a nearby building, aimed his rifle, and picked off police officers as the panic-stricken crowd scattered.

Police say the African-American man declared to them that he was angered by the police shootings and wanted to kill white people. After a standoff, Johnson was killed with the first-known U.S. use of a bomb-deploying robot.

Protesters also gathered at the U.S. Capitol in Washington where they sang the civil-rights anthem, "We Shall Overcome." Across the street, inside a reading room of the Library of Congress, the sound of bullets smashed the silence as African-American library employees watched cellphone videos of the latest deaths gone viral.

The New York Times ran a weary letter from the mother of Michael Brown. His death in Ferguson, Mo., sparked the Black Lives Matter movement. The two years since have spurred an increase in the use of body cameras, more charges against officers, and data-gathering efforts that have begun showing how blacks are statistically far likelier to be killed by police.

Yet Brown's mother, Lezlie McSpadden, expressed cynicism on two fronts. She said police don't get convicted, and the dead get blamed: "These men will be called 'thugs' and much, much worse," she wrote in the Times. "You will be shocked by the racist comments of people who insist -- insist -- that they obviously deserved to die."

Gun-control advocates link these cases to the country's uniquely vast proliferation of firearms.

A study in the American Journal of Public Health suggests U.S. police officers may have reason for jitters around their well-armed citizenry. It concluded that officers in major gun-owning states were three times likelier to be killed.

The part of this country favouring gun control regularly points out statistics like these -- or the one showing a 10 times higher rate of gun crimes here per capita than in Canada and 60 times higher rate than in the U.K.

Mass-shootings here are so common that they regularly play havoc with the political calendar. Last month, Hillary Clinton cancelled her first scheduled rally with the president because of the Orlando massacre. This week, she cancelled her first rally with the vice-president because of Dallas. President Barack Obama, in Europe for a NATO summit, is returning home a day early to visit the city.

The other America draws from different statistics.

It sees homicide rates being far higher in Mexico, Russia and Brazil, and fumes at the media for never mentioning this. It wonders why people keep discussing the 258 black people killed by police last year, according to a new Washington Post database, but never the 494 whites.

The NRA magazine, "America's First Freedom," reflects that other America: more rural, more conservative, more white.

Its latest issue has ads for NASCAR, for diamond-encrusted rings with military logos, and features 36 photos of white people, one of Nikki Haley, the Indian-American governor of South Carolina, and zero of anyone who looks like Philando Castile.

It shares the perspectives of gun-owning, law-abiding Americans who say they're the ones being persecuted.

One piece opens with gun-owners feeling belittled and lied about -- by politicians, pundits, Hollywood and the media. It shares the anecdote of someone moving to the author's small town from New York City, and calling the police, alarmed, upon hearing gunfire: "The officer who showed said, 'Welcome to the country.' He might as well have said, 'Welcome to the other half of America."'

This half of America is upset with President Obama.

He'd made comments about the week's earlier events. Obama defended police as mostly good, but cited statistics about how much likelier it was for African-Americans to be pulled over: "This is not just a black issue. It's not just an Hispanic issue. This is an American issue that we should all care about."

Within hours, pandemonium struck in Dallas.

Once again, two different Americas have revealed themselves in the aftermath.

In this combustible atmosphere, some lit a match. A few online commentators celebrated the shootings. More than a few tore into Obama. One former Illinois congressman laced into him with several tweets including one he deleted: "This is now war. Watch out Obama. Watch out black lives matter punks. Real America is coming after you."

Others sought to soothe. This group included a rumoured possible running mate to Donald Trump. Newt Gingrich said it took him many years, and many conversations, to recognize that white Americans often fail to understand the fear and discrimination felt by black Americans.

The mayor of Dallas addressed all these people.

Mike Rawlings said his generation of leaders had failed to salve old wounds that festered for centuries. He urged everyone to choose their words carefully over the next while.

"We must love one another," he said.

"Because if we don't this cancer of separatism will kill this body."